Methods and systems for estimating the melting temperature (TM) for polynucleotide molecules

ABSTRACT

The invention relates to methods and systems for predicting or estimating the melting temperature of duplex nucleic acids, particularly duplexes of oligonucleotides which may be used, for example, as primers or probes in PCR and/or hybridization assays. The invention also relates to methods and systems for designing and selecting oligonucleotide probes and primers having a predicted melting temperature which is optimized for such assays. To this end, algorithms and methods are provided for predicting the melting temperature of a nucleic acid having a predetermined sequence. These methods and algorithms estimate the melting temperature of a nucleic acid duplex under particular salt conditions. The methods and algorithms use novel formulas, having terms and coefficients that are functions of the particular nucleotide sequence, to estimate the effect of particular salt conditions on the melting temperature. As such, the methods and systems of the invention provide superior result compared to existing methods, which do not consider sequence dependent effects of changing salt conditions.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] Priority is claimed under 35 U.S.C. 119(e) to U.S. provisionalapplication Serial No. 60/410,663 filed on Sep. 12, 2002, the entirecontents of which is incorporated herein by reference, in its entirety.

FIELD OF THE INVENTION

[0002] The present invention relates to methods for the design, analysisand/or evaluation of nucleic acid molecules, particular oligonucleotidenucleic acids (also referred to as “oligomers”). The invention alsorelates to the design, analysis and/or evaluation of nucleic acids forparticular uses or applications. For example, in particular embodimentsthe invention relates to methods for designing oligonucleotide probesand primers, e.g., for use in PCR or on microarrays. The invention stillfurther relates to systems, including computer systems and computerprogram products which may be used to practice the particular methods ofthis invention and/or to program a computer to implement such methods.

BACKGROUND OF THE INVENTION

[0003] Hybridization between complementary nucleic acids is an implicitfeature in the Watson-Crick model for DNA structure that is exploitedfor many applications of the biological and biomedical arts. Forexample, virtually all methods for replicating and/or amplifying nucleicacid molecules are initiated by a step in which a complementaryoligonucleotide (typically referred to as a “primer”) hybridizes to someportion of a “target” nucleic acid molecule. A polymerase thensynthesizes a complementary nucleic acid from the primer, using thetarget nucleic acid as a “template”. See, Kleppe et al., J. Mol. Biol.1971, 56:341-361.

[0004] One particular application, known as the polymerase chainreaction (PCR), is widely used in a variety of biological and medicalarts. For a description, see Saiki et al., Science 1985, 230:1350-1354.In PCR, two or more primers are used that hybridize to separate regionsof a target nucleic acid and its complementary sequence. The sample isthen subjected to multiple cycles of heating and cooling, repeatedlyhybridizing and dissociating the complementary strands so that multiplereplications of the target nucleic acid and its complement areperformed. As a result, even very small initial quantities of a targetnucleic acid may be enormously increased or “amplified” for subsequentuses (e.g., for detection, sequencing, etc.).

[0005] Multiplex PCR is a particular version of PCR in which severaldifferent primers are used to amplify and detect a plurality ofdifferent nucleic acids in a sample—usually ten to a hundred differenttarget nucleic acids. Thus, the technique allows a user tosimultaneously amplify and evaluate large numbers of different nucleicacids simultaneously in a single sample. The enormous benefits of highthroughput, speed and efficiency offered by this technique has mademultiplex PCR increasingly popular. However, achievement of successfulmultiplex PCR usually involves empirical testing as existing computerprograms that pick and/or design PCR primers have errors. In multiplexPCR, the errors become additive and therefore good results are seldomachieved without some amount of trial and error. Markouatos et al., J.Clin. Lab Anal. 2002, 16(1):47-51; Henegarin et al., Biotechniques 1997,23(3):504-11.

[0006] Other techniques that are widely used in the biological andmedical arts exploit nucleic acid hybridization to detect target nucleicacid sequences in a sample. See, for example, Southern, J. Mol. Biol.1975, 98:503-517; Denhardt, Biochem. Biophys. Res. Commun. 1966,23:641-646; Meinhoth & Wahl, Anal. Biochem. 1984, 138:267-284. Forinstance, Southern blotting and similar techniques have long been usedin which nucleic acid molecules from a sample are immobilized onto asolid surface or support (e.g., a membrane support). A target nucleicacid molecule of interest may then be detected by contacting one or morecomplementary nucleic acids (often referred to as a nucleic acid“probes”) and detecting their hybridization to nucleic acid molecules onthe surface or support (for example, through a signal generated by somedetectable label on the probes).

[0007] Similar techniques are also known in which one or more nucleicacid probes are immobilized onto a solid surface or support, and asample of nucleic acid molecules is hybridized thereto. Nucleic acidarrays, for example, are known and have become increasingly popular inthe art. See, e.g., DeRisi et al., Science 1997, 278:680-686; Schena etal., Science 1995, 270:467-470; and Lockhart et al., Nature Biotech.1996, 14:1675. See also, U.S. Pat. No. 5,510,270 issued Apr. 23, 1996 toFodor et al. Nucleic acid arrays typically comprise a plurality (oftenmany hundreds or even thousands) of different probes, each immobilizedat a defined location on the surface or support. A sample of nucleicacids (for example, an mRNA sample, or a sample of cDNA or cRNA derivedtherefrom) that are preferably detectably labeled may then be contactedto the array, and hybridization of those nucleic acids to the differentprobes may be assessed, e.g., by detecting labeled nucleic acids at eachprobe's location on the array. Thus, hybridization techniques usingnucleic acid arrays have the potential for simultaneously detecting alarge number of different nucleic acid molecules in a sample, bysimultaneously detecting their hybridization to the different probes ofthe array.

[0008] The successful implementation of all techniques involving nucleicacid hybridization (including the exemplary techniques described, supra)is dependent upon the use of nucleic acid probes and primers thatspecifically hybridize with complementary nucleic acids of interestwhile, at the same time, avoiding non-specific hybridization with othernucleic acid molecules that may be present. For a review, see Wetmur,Critical Reviews in Biochemistry and Molecular Biology 1991, 26:227-259.These properties are even more critical in techniques, such as multiplexPCR and microarray hybridization, where a plurality of different probesor primers is used, each of which is preferably specific for a differenttarget nucleic acid.

[0009] Duplex stability between complementary nucleic acid molecules isfrequently expressed by the duplex's “melting temperature” (T_(m)).Roughly speaking, the T_(m) indicates the temperature at which a duplexnucleic acid dissociates into single-stranded nucleic acids. Preferably,nucleic acid hybridization is performed at a temperature slightly belowthe T_(m), so that hybridization between a probe or primer and itstarget nucleic acid is optimized, while minimizing non-specifichybridization of the probe or primer to other, non-target nucleic acids.Duplex stability and T_(m) are also important in applications, such asPCR, where thermocycling may be involved. During such thermocyclingsteps, it is important that the sample temperature be raisedsufficiently above the T_(m) so that duplexes of the target nucleic acidand its complement are dissociated. In subsequent steps of reannealing,however, the temperature must be brought sufficiently below the T_(m)that duplexes of the target nucleic acid and primer are able to form,while still remaining high enough to avoid non-specific hybridizationevents. For a general discussion, see Rychlik et al., Nucleic AcidsResearch 1990, 18:6409-6412.

[0010] Traditionally, theoretical or empirical models that relate duplexstability to nucleotide sequence have been used to predict or estimatemelting temperatures for particular nucleic acids. For example,Breslauer et al. (Proc. Natl. Acad. Sci. U.S.A. 1986, 83:3746-3750)describe a model for predicting melting temperatures that is widely usedin the art, known as the “nearest neighbor model”. See also, SantaLuciaet al., Biochemistry 1996, 35:3555-3562; and SantaLucia, Proc. Natl.Acad. Sci. U.S.A. 1998, 95:1460-1465. Such models are usually calibratedor optimized for particular salt conditions, typically 1 M Na⁺. However,applications that exploit nucleic acid hybridization may be implementedin a variety of different salt conditions, with cation concentrationstypically being on the order of magnitude of 10-100 mM. Thus, meltingtemperatures for particular probes or primers in an assay are typicallypredicted by predicting a melting temperature at a first saltconcentration using the nearest neighbor or other model, and then usinganother theoretical or empirical model to predict what effect(s) thesalt conditions of the particular assay will have on that meltingtemperature.

[0011] Most, if not all of the existing models used to estimate T_(m)treat the effects of salt concentration as being separate from andindependent of the nucleotide sequence. For example, Schildkraut et al.(Biopolymers 1965, 3:195-208) proposed the following formula to estimatenucleic acid melting temperatures at different sodium ionconcentrations, [Na⁺]:

T _(m)([Na⁺])=T _(m) ⁰+16.6×log [Na⁺]  (Equation 1.1)

[0012] where T_(m) ⁰ is the melting temperature of the DNA duplex in 1 Msodium ions. Equation 1.1, above, is based on empirical data from thespecific study of Escherichia coli genomic DNA in buffer of between0.01-0.2 M Na⁺. Nevertheless, the use of this equation has beenroutinely generalized to model any DNA duplex oligomer pair. See, forexample, Rychlik et al., Nucleic Acids Res. 1990, 18:6409-6412, Ivanov &AbouHaidar, Analytical Biochemistry 1995, 232:249-251; Wetmur, CriticalReview in Biochemistry and Molecular Biology 1991, 26:227-259.

[0013] There is evidence, however, indicating that the effects of saltconcentration on the melting temperature of nucleotide duplexes are notsequence independent but, rather, depend substantially on sequencecomposition of the particular nucleic acids. For a review see,Bloomfield et al., Nucleic Acids: Structure, Properties, and Functions(University Science Books, Sausalito California 2000): pages 307-308.For example, Owen et al. (Biopolymers 1969, 7:503-516) have proposed oneempirical formula, based on melting experiments of bacterial DNA, thatrelates melting temperature (T_(m)) of long polymeric DNAs to log [Na⁺]and the nucleic acid's G-C content, ƒ(G-C):

ƒ(G-C)=tan(70.077+3.32×log [Na⁺])×(T _(m)−175.95)+260.34   (Equation1.2)

[0014] Still others (Frank-Kamenetskii, Biopolymers 1971, 10:2623-2624)have reanalyzed the same experimental data and suggested simplifiedequations, purportedly reflecting the linear dependence of meltingtemperature on log[Na⁺]:

T _(m)=176.0−(2.60−ƒ(G-C))×(36.0−7.04×log [Na⁺])   (Equation 1.3)

[0015] Doktycz et al. (Biopolymers 1992, 32:849-864) have appliedEquation 1.3, above, to estimate the salt dependence of T_(m) foraverage G-C and A-T base pairs in a DNA duplex, and concludes that thedependence is governed by different equations for each type of basepair. Blake & Delcourt (Nucl. Acids Res. 1998, 26:3323-3332;Corrigendum, Nucl. Acids Res. 1999, 27, No.3) also report that the rateat which T_(m) changes as a linear function of log [Na⁺] varies witheach nearest neighbor, based on melting curves of synthetic tandemlyrepeating nucleic acid inserts in recombinant pN/MCS plasmids. However,their experiments were conducted in the narrow range of Na⁺concentrations from 34 mM to 114 mM.

[0016] Rouzina & Bloomfield (Biophysical Journal 1999, 77:3242-3251)have also analyzed melting data from large, polymeric DNA molecules andpropose an alternative interpretation for the salt dependence of meltingtemperatures. In particular, the publication suggests a new explanationof empirical Frank-Kamenetskii's relationship (Equation 1.3) that saltdependence of T_(m) may be due to small differences between the heatcapacities of duplex and single-stranded nucleic acid molecules insolution. The publication suggests that this effect may be at leastpartially sequence dependent. Yet, no new relationship betweennucleotide sequence and the effect is proposed or suggested.

[0017] Finally, Owczarzy et al., Biopolymers 1997, 44:217-239 describeexperiments evaluating melting temperatures for oligonucleotide duplexeswith various G-C content,ƒ(G-C). However, melting temperatures wereevaluated at only two concentrations of sodium ions, 1 M and 115 mM.Consequently, the publication provides an equation that only predictsT_(m) values between those two conditions.

[0018] Despite the existence of such data, sequence-independent formulassuch as Equations 1.1, supra, are still used in the art to estimatesalt-corrected melting temperatures. For instance, as recently as 1998SantaLucia et al. (Proc. Natl. Acad. Sci. U.S.A. 1998, 95:1460-1465)have advocated formulas that estimate salt dependence of a meltingtemperature by assuming the effects are sequence independent. Thus, eventhough there may be data suggesting that the effects of salt on anucleic acid's melting temperature depend on the nucleotide sequence,the available data is incomplete and, in many instances, obtained underconditions which are, at best, remote from those of biological orbiomedical techniques that involve nucleic acid hybridization.Specifically, effects of sodium ions on Tm have been systematicallystudied only for long DNA polymers and DNA dumbbells. See Blake &Delcourt, Nucl. Acids Res. 1998, 26:3323-3332 and Doktycz et al.(Biopolymers 192, 32:849-864). As a result, the exact effect saltconditions will have on a probe or primer's melting temperature in suchassays remains poorly characterized and unknown. Consequently, currentlyavailable methods for estimating melting temperatures of particularprobe or primer sequences in hybridization assays are inaccurate andunreliable.

[0019] Yet, given the prevalence and importance of such assays in thebiological and biomedical arts, there is a significant need for methodsof estimating and predicting melting temperatures with improvedaccuracy. In particular, there is a need for methods which predict orestimate the melting temperature for a nucleic acid, particularly for anoligonucleotide (e.g., an oligonucleotide probe or primer) in a PCR orother assay that involve nucleic acid hybridization. There exists,moreover, a need for reliable and accurate methods that estimate effectsof changing salt concentration on the melting temperature of particularnucleic acid sequences. There further exists a need for methods ofdesigning oligonucleotides, e.g., as probes or primers for a particularhybridization, PCR or other method, in which the melting temperature ofeach oligonucleotide is optimized for the particular method or assay.

[0020] The citation or discussion of any reference in this section orelsewhere in the specification is made only to clarify the descriptionof the present invention and is not an admission that any such referenceis “prior art” against any invention described herein.

SUMMARY OF THE INVENTION

[0021] Applicants have discovered a method for estimating a meltingtemperature for a polynucleotide and its complementary sequence in aparticular salt condition. The method is directed to obtaining areference melting temperature at a reference salt concentration and thencalculating, from the reference temperature in a manner that isdependent on the G-C content of the polynucleotide, a new salt dependent“corrected” melting temperature. The invention provides a novel methodfor reliably estimating melting temperatures for polynucleotides at adesired salt concentration. The method is straightforward and iscomputationally tractable.

[0022] Accordingly, a skilled artisan can readily use the method toestimate polynucleotide melting temperatures under particular saltconditions and/ or adjust salt conditions for an assay. In addition, askilled artisan can readily use the method to estimate meltingtemperatures for a variety of different polynucleotide probes and/orprimers in desired salt conditions and those probes and/or primershaving optimal melting temperatures may then be selected.

[0023] The method therefore provides for obtaining a reference meltingtemperature for a particular nucleic acid at a reference saltconcentration. Accordingly, a skilled artisan can readily usetheoretical, empirical or semi-empirical methods to obtain an accurateor reliable reference melting temperature. The method also provides fora desired salt concentration. A skilled artisan will readily obtain adesired salt concentration based upon the polynucleotide meltingconditions of interest to the artisan. More specifically, the methodprovides for using the reference polynucleotide melting temperature toestimate or determine a salt-dependent, “corrected” melting temperaturein a manner that is dependent on the G-C content of the polynucleotide.It is further provided that the G-C content can be used by a skilledartisan to determine a G-C content value.

[0024] The method of the present invention provides for the use offormulas which may be used to implement the method of the invention. Theformulas elucidate the relationship of the reference meltingtemperature, the desired salt concentration and the G-C content value inthe estimation of the salt “corrected” melting temperature. Accordinglya skilled artisan may readily estimate the desired melting temperatureof a polynucleotide using the method of the present invention. Inaddition, optimized coefficients derived from experimentally measureddata are provided for use with the formulations.

[0025] Computer systems are also provided that may be used to implementthe analytical methods of the invention, including methods of estimatinga salt-corrected melting temperature of a polynucleotide. These computersystems comprise a processor interconnected with a memory that containsone or more software components. In particular, the one or more softwarecomponents include programs that cause the processor to implement stepsof the analytical methods described herein. The software components maycomprise additional programs and/or files including, for example,sequence or structural databases of polymers.

[0026] Computer program products are further provided, which comprise acomputer readable medium, such as one or more floppy disks, compactdiscs (e.g., CD-ROMS or RW-CDS), DVDs, data tapes, etc., that have oneor more software components encoded thereon in computer readable form.In particular, the software components may be loaded into the memory ofa computer system and may then cause a processor of the computer systemto execute steps of the analytical methods described herein. Thesoftware components may include additional programs and/or filesincluding databases, e.g., of polymer sequences and/or structures.

BRIEF DESCRIPTION OF DRAWINGS

[0027]FIG. 1A shows a UV-melting curve for a 2 μM solution of theoligonucleotide 5′-TAACCATACTGAATACCTTTTGACG-3′ (SEQ ID NO: 45) and itscomplement dissolved in 68.9 mM Na⁺ buffer.

[0028]FIG. 1B shows a differential scanning calorimetry (DSC) curve fora 90 μM solution of the oligonucleotide 5′-TAACCATACTGAATACCTTTTGACG-3′(SEQ ID NO:45) and its complement dissolved in 68.9 mM Na⁺ buffer.

[0029]FIG. 2 shows an exemplary computer system that may be used toimplement the analytical methods of the invention. FIG. 3 shows theslope obtained for each of a plurality of different oligomers (SEQ IDNOS:1-80) whose experimentally determined melting temperatures (T_(m)'s)are fit to a linear function of log [Na⁺], plotted as a function of eacholigomer's G-C content ƒ(G-C). Melting temperatures for each oligomerwere measured in estimated sodium cation concentrations of 68.9, 220,621 and 1020 mM and are set forth in Table I, infra.

[0030]FIG. 4 shows the slopes, as a function of G-C content ƒ(G-C),obtained where the inverse of experimentally determined meltingtemperatures (i.e. 1/T_(m)) for each of the plurality of differentoligomers (SEQ ID NOS: 1-80) are fit to a linear function of log [Na⁺].

DETAILED DESCRIPTION OF THE INVENTION

[0031] Definitions:

[0032] The term “melting profile” refers to a collection of measurementsof an oligonucleotide and its complement which indicate theoligonucleotide molecule's transition from double-stranded tosingle-stranded nucleic acid (or vice-versa). The transition of anucleic acid from double-stranded to single-stranded is often describedin the art as the “melting” of that nucleic acid molecule. Thetransition may also be described as the “denaturation” or “dissociation”of the nucleic acid. Accordingly, a melting profile of the presentinvention may also be referred to as a “dissociation profile”, a“denaturation profile”, a “melting curve”, a “dissociation curve”, etc.

[0033] The term “salt concentration” is interchangeably used with theterm “ion concentration” and refers, specifically, to the concentrationof cations (i.e., positively charged ions within a sample). Types ofions include, but are not limited to, lithium, potassium, sodium,rubidium, cesium and francium. Ions may carry a single or multiplecharge. A preferred embodiment of the invention is the use of monovalentions. It is preferred that the ion concentration ranges from about 1 mMto about 5 M. It is more preferred, however, that the ion concentrationrange from about 5 mM to about 2 M. In particularly preferredembodiments, the ion concentration ranges from about 70 mM to about 1020mM.

[0034] The “melting temperature” or “T_(m)” of a nucleic acid moleculegenerally refers to the temperature at which a polynucleotidedissociates from its complementary sequence. Generally, the T_(m) may bedefined as the temperature at which one-half of the Watson-Crick basepairs in duplex nucleic acid molecules are broken or dissociated (i.e.,are “melted”) while the other half of the Watson-Crick base pairs remainintact in a double stranded conformation (i.e., the fraction of brokenbased pairs, θ(T)=0.5 when T=T_(m)). In preferred embodiments whereduplex nucleic acid molecules are oligonucleotides and in otherembodiments where the duplex nucleic acids dissociate in a two-statefashion, the T_(m) of a nucleic acid may also be defined as thetemperature at which one-half of the nucleic acid molecules in a sampleare in a single-stranded conformation while the other half of thenucleic acid molecules in that sample are in a double-strandedconformation. T_(m), therefore defines a midpoint in the transition fromdouble-stranded to single-stranded nucleic acid molecules (or,conversely, in the transition from single-stranded to double-strandednucleic acid molecules).

[0035] It is well appreciated in the art that the transition fromdouble-stranded to single-stranded nucleic acid molecules does not occurat a single temperature but, rather, over a range of temperatures.Nevertheless, the T_(m) provides a convenient measurement forapproximating whether nucleic acid molecules in a sample exist in asingle-stranded or double-stranded conformation. As such, the meltingtemperature of a nucleic acid sample may be readily obtained by simplyevaluating a melting profile for that sample.

[0036] The methods and algorithms of this invention involve calculatingestimated melting temperatures for complementary nucleic acids and canbe applied generally to any of the various types of nucleic acids,including but not limited to DNA, RNA, mRNA, cDNA, and cRNA, as well as“protein nucleic acids” (PNA) formed by conjugating bases to an aminoacid backbone. Polynucleotides that may be used in accordance with thepresent invention also include double stranded DNA and RNA duplexoligomers, single stranded DNA and RNA, as well as backbonemodifications thereof (for example, methylphosphonate linkages). Thisalso includes nucleic acids containing modified bases, for example,thio-uracil, thio-guanine and fluoro-uracil.

[0037] The nucleic acids may also be modified by many means known in theart. Non-limiting examples of such modifications include methylation,“caps”, substitution of one or more of the naturally occurringnucleotides with an analog, and internucleotide modifications such as,for example, those with uncharged linkages (e.g., methyl phosphonates,phosphotriesters, phosphoroamidates, carbamates, etc.) and with chargedlinkages (e.g., phosphorothioates, phosphorodithioates, etc.).Polynucleotides may contain one or more additional covalently linkedmoieties, such as proteins (e.g., nucleases, toxins, antibodies, signalpeptides, poly-L-lysine, etc.), intercalators (e.g., acridine, psoralen,etc.), chelators (e.g., metals, radioactive metals, iron, oxidativemetals, etc.) and alkylators to name a few. The polynucleotides may bederivatized by formation of a methyl or ethyl phosphotriester or analkyl phosphoramidite linkage. Furthermore, the polynucleotides hereinmay also be modified with a label capable of providing a detectablesignal, either directly or indirectly. Exemplary labels includeradioisotopes, fluorescent molecules, biotin and the like.

[0038] As used herein, the terms “polynucleotide” and “oligonucleotide”are interchangeable and are generally used to describe nucleic acidpolymers typically having no more than about 500 base pairs. Inpreferred embodiments, the present invention is practiced usingoligonucleotides between about 5 and 150 nucleotides in length, and morepreferably between about 10 and 30 nucleotides in length.Oligonucleotides used in the present invention may hybridize to any typeof nucleic acid from any source; including but not limited to genomicDNA, mRNA, cDNA, Expressed Sequence Tags (ESTs), and chemicallysynthesized nucleic acids. Oligonucleotides of the invention may alsohybridize to other oligonucleotide molecules.

[0039] Oligonucleotides and other polynucleotides can be labeled, e.g.,with ³²P-nucleotides or nucleotides to which a label, such as biotin ora fluorescent dye (for example, Cy3 or Cy5) has been covalentlyconjugated. Generally, oligonucleotides are prepared synthetically,preferably on a nucleic acid synthesizer. Accordingly, oligonucleotidescan be prepared with non-naturally occurring phosphoester analog bonds,such as thioester bonds, etc.

[0040] A pair of hybridized polynucleotides may be complementary alongtheir entire length or, alternatively, along only a part of theirsequence. In preferred embodiments, all of the nucleotides in a pair ofhybridized oligonucleotides are complementary. However, mismatch basepairing between complementary nucleic acids may occur, and such nucleicacids are therefore said to be less than 100% complementary. Inparticular, the extent of complementarity is usually indicated by thefraction (e.g., the percentage) of mismatched base pairs out of thetotal number of base pairs in the complementary polynucleotides. It isvery preferred that there is at least 99% complementarity between thepolynucleotide and its complementary sequence. However, lesscomplementarity may be acceptable or even desirable in some embodiments.For example, in some embodiments, the level of complementary may be aslow as 95%, 85% or 75%.

[0041] In preferred embodiments, the terms “about” and “approximately”shall generally mean an acceptable degree of error for the quantitymeasured given the nature or precision of the measurements. Typical,exemplary degrees of error are within 20 percent (%), preferably within10%, and more preferably within 5% of a given value or range of values.Alternatively, and particularly in biological systems, the terms “about”and “approximately” may mean values that are within an order ofmagnitude, preferably within 5-fold and more preferably within 2-fold ofa given value. Numerical quantities given herein are approximate unlessstated otherwise, meaning that the term “about” or “approximately” canbe inferred when not expressly stated.

[0042] A nucleic acid molecule is “hybridizable” to another nucleic acidmolecule, such as a cDNA, genomic DNA, or RNA, when a single strandedform of the nucleic acid molecule can anneal to the other nucleic acidmolecule under the appropriate conditions of temperature and solutionionic strength (see Sambrook et al., supra). The conditions oftemperature and ionic strength determine the “stringency” of thehybridization. Hybridization requires that the two nucleic acids containcomplementary sequences. However, mismatches between bases are possibledepending on the stringency of the hybridization conditions. Theappropriate stringency for hybridizing nucleic acids depends on thelength of the nucleic acids and the degree of complementarity, variableswell known in the art. The greater the degree of similarity or homologybetween two nucleotide sequences, the greater the value of T_(m) forduplexes of nucleic acids having those sequences. For duplexes ofgreater than 100 nucleotides in length, equations for calculating T_(m)have been derived (see Sambrook et al., supra, 9.50-9.51). Forhybridization with shorter nucleic acids, i.e., oligonucleotides, theposition of mismatches becomes more important, and the length of theoligonucleotide determines its specificity (see Sambrook et al., supra,11.7-11.8). A minimum length for a hybridizable nucleic acid is at leastabout 10 nucleotides; preferably at least about 15 nucleotides; and morepreferably the length is at least about 20 nucleotides. Unless otherconditions are specified, the term “standard hybridization conditions”refers to a T_(m) of about 55° C., and utilizes conditions as set forthabove. In a preferred embodiment, the T_(m) is 60° C.; in a morepreferred embodiment, the T_(m) is 65° C. In a specific embodiment,“high stringency” refers to hybridization and/or washing conditions at68° C. in 0.2×SSC, at 42° C. in 50% formamide, 4×SSC, or underconditions that afford levels of hybridization equivalent to thoseobserved under either of these two conditions.

[0043] Suitable hybridization conditions for oligonucleotides (e.g., foroligonucleotide probes or primers) are typically somewhat different thanfor full-length nucleic acids (e.g., full-length cDNA), because of theoligonucleotides' lower melting temperature. Because the meltingtemperature of oligonucleotides will depend on the length of theoligonucleotide sequences involved, suitable hybridization temperatureswill vary depending upon the oligonucleotide molecules used. Exemplarytemperatures may be 37° C. (for 14-base oligonucleotides), 48° C. (for17-base oligonucleotides), 55° C. (for 20-base oligonucleotides) and 60°C. (for 23-base oligonucleotides). Exemplary suitable hybridizationconditions for oligonucleotides include washing in 6×SSC/0.05% sodiumpyrophosphate, or other conditions that afford equivalent levels ofhybridization.

[0044] Nucleic acids can be purified by precipitation, chromatography(including preparative solid phase chromatography), oligonucleotidehybridization, ultracentrifugation, and other means. In one method,nucleic acids are purified using polyacrylamide gel purification (PAGE)techniques. In another preferred embodiment, they are purified usinghigh pressure liquid chromatography (HPLC). Such methods of purificationare also well known in the art.

[0045] General Methods:

[0046] In accordance with the invention, there may be employedconventional molecular biology, microbiology and recombinant DNAtechniques within the skill of the art. Such techniques are explainedfully in the literature. See, for example, Sambrook, Fitsch & Maniatis,Molecular Cloning. A Laboratory Manual, Second Edition (1989) ColdSpring Harbor Laboratory Press, Cold Spring Harbor, New York (referredto herein as “Sambrook et al., 1989”); DNA Cloning. A PracticalApproach, Volumes I and II (D. N. Glover ed. 1985); OligonucleotideSynthesis (M. J. Gait ed. 1984); Nucleic Acid Hybridization (B. D. Hames& S. J. Higgins, eds. 1984); Animal Cell Culture (R. I. Freshney, ed.1986); Immobilized Cells and Enzymes (IRL Press, 1986); B. E. Perbal, APractical Guide to Molecular Cloning (1984); F. M. Ausubel et al.(eds.), Current Protocols in Molecular Biology, John Wiley & Sons, Inc.(1994).

[0047] This invention pertains to a method for predicting the meltingtemperature at a specific ion concentration for a polynucleotide havinga G-C content. This invention can be applied to the design ofoligonucleotide probes, hybridization and PCR methods, and microarrayhybridization methods.

[0048] Overview of the Method:

[0049] In accordance with the present invention, methods are providedhere for estimating a melting temperature (T_(m)) for a polynucleotideor, more specifically, for a polynucleotide and its complementarysequence. Such methods are particularly well suited for the design ofoligonucleotide probes and primers, e.g., for use in biological assayssuch as PCR and nucleic acid hybridization assays. The methods of theinvention are robust and straightforward, and provide reliablepredictions or estimations of melting temperatures for polynucleotidesunder conditions that are typically used in such assays. In particular,using the methods of the invention a skilled artisan may readilydetermine or estimate melting temperatures for polynucleotides underparticular salt conditions and/or may adjust salt conditions for anassay accordingly. Alternatively, the methods of the invention may beused to determine or estimate melting temperatures for a variety ofdifferent polynucleotide probes and/or primers in desired saltconditions, and those probes and/or primers having optimal meltingtemperatures for the assay may then be selected. In its simplest form,the method of the invention comprises a step of obtaining or determininga “reference” melting temperature for a polynucleotide in a particularsalt concentration (i.e., the “reference” salt concentration). Thereference temperature may then be used in accordance with the presentinvention to obtain or estimate a “salt-corrected” melting temperaturetherefrom. More specifically, the salt-corrected melting temperature maybe derived from the reference melting temperature according to arelationship that is dependent upon the polynucleotide's G-C sequencecontent. A more detailed description of these methods follows below.

[0050] Reference melting temperature. A reference melting temperature,typically denoted here by the symbol T_(m) ⁰, may be readily obtainedfor a particular nucleic acid using any technique known in the art forobtaining or determining melting temperatures. For example, meltingtemperatures may be experimentally determined for one or morepolynucleotides (as described in the Examples, infra) at some standardor reference salt concentration, and these empirically determinedmelting temperatures may then be used as reference melting temperaturesin accordance with the present invention. However, a reference meltingtemperature may also be obtained or provided using theoretical,empirical or semi-empirical models that predict melting temperatures atsome salt concentration. In particularly preferred embodiments, thereference melting temperature for a polynucleotide is obtained using the“nearest neighbor model”, which is well known in the art (see, e.g.,Breslauer et al., Proc. Natl. Acad. Sci. U.S.A. 1986, 83:3746-3750; andSantaLucia et al., Proc. Natl. Acad. Sci. U.S.A. 1998, 95:1460).However, various other models are known in the art and may also be usedin accordance with the present invention.

[0051] The exact experimental method, model or formula used to obtainthe reference melting temperature is not crucial for practicing theinvention. For example and as noted above, the reference meltingtemperature may be determined empirically; e.g., by using the meltingtemperature of a polynucleotide duplex at some reference saltconcentration. However, the melting temperature may also be calculatedusing some theoretical, empirical or semi-empirical model. The modelwill preferably provide an ‘accurate’ or reliable estimate of themelting temperature at some salt concentration for which the model hasbeen optimized. For example, the nearest neighbor model and many othermodels for predicting melting temperatures use parameters that have beenparticularly optimized for a 1 M concentration of monovalent cations(specifically, for 1 M Na⁺). Accordingly, in embodiments where suchmodels are used to obtain a reference melting temperature, the referencesalt concentration is preferably 1 M. Generally, those skilled in theart will readily appreciate for what salt concentrations a method ormodel for obtaining melting temperatures has been optimized and,accordingly, will be able to use those salt concentrations as the“reference” salt concentration (denoted herein by the symbol [X⁺]₀) forpracticing the methods of this invention.

[0052] Salt concentration. In accordance with the methods of thisinvention, the melting temperature of a polynucleotide may be readilydetermined for a particular salt concentration (denoted [X⁺]) ofinterest to a user. Generally, the salt concentration of interest willcorrespond to salt conditions for a biological assay (e.g. a PCR orhybridization assay) of particular interest to the user. In preferredembodiments of the invention, the salt concentration of interest will bea concentration of sodium ions. However, other monovalent cations (e.g.,potassium, lithium, rubidium, cesium and francium) may be substitutedfor sodium. In many hybridization assays only monovalent cations arepresent. However, divalent cations such as magnesium may also bepresent. If divalent cations are present, melting temperatures may bedetermined using the methods described below for monovalent cations andthen adjusted for divalent ion concentrations, e.g., using techniquesthat are already known in the art. See, for example, Ahsen et al.,Clinical Chemistry 2001, 47:1956-1961, see also Peyrot N. (2000)“Prediction of Nucleic Acid Hybridization: Parameters and Algorithm,”Ph.D. Thesis, Wayne State University, Detroit, Mich.

[0053] As demonstrated in the Examples, infra, the methods of theinvention are robust, and may be used reliably to determine meltingtemperatures for a wide range of different salt conditions. Preferredconcentrations may be anywhere from about 5 mM to about 2 M, and aremore preferably between about 50 mM and 1 M. In particularly preferredembodiments, a salt concentration of interest will be between about 70and about 1020 mM. However, using empirical techniques that aredemonstrated in the below examples, a skilled artisan can readilyoptimize the formulas and methods of this invention for any saltconcentration or range of salt concentrations of interest. Accordingly,the formulas and techniques described here need not be limited to thespecific ranges of salt concentration used in those examples.

[0054] G-C content value. The invention provides methods and formulaswhich more accurately estimate salt effects on the melting temperatureof a polynucleotide. In particular, these methods adjust the “reference”melting temperature T_(m) ⁰ in a manner that is dependent upon thepolynucleotide's sequence content, specifically the content of guanine(G) and cytosine (C) base pairs that form between a polynucleotide andits complement. Accordingly, the systems and methods of the inventionalso use a value, referred to herein as the “G-C content value” anddenoted by the symbol ƒ(G-C). The G-C content value ƒ(G-C) provides anumerical value which is indicative of the number of G-C base pairsformed between a polynucleotide and its complementary sequence. Inpreferred embodiments, the G-C content of a polynucleotide may beobtained or provided from the molar fraction of G-C base pairs in thepolynucleotide duplex; i.e., ƒ(G-C)=(no. G-C base pairs)/(total no. basepairs).

[0055] Estimating Salt Dependent Effects of Melting Temperature (T_(m)):

[0056] In accordance with the present invention, Applicants havediscovered novel relationships between the melting temperature of apolynucleotide (T_(m)), the salt concentration [X⁺] in which thepolynucleotide dissociation (or hybridization) occurs, and thepolynucleotide's G-C content value ƒ(G-C). Accordingly, the inventionprovides novel methods for estimating melting temperatures using thesenovel relationships. Generally speaking, a “reference” meltingtemperature T_(m) ⁰ is obtained or provided for the polynucleotide at a“reference” salt concentration [X⁺]₀, as described above. The referencemelting temperature is then used to calculate a salt-corrected T_(m)according to a relationship that has been optimized for thepolynucleotide's G-C content.

[0057] For example, in one preferred embodiment, a salt-correctedmelting temperature (T_(m)) may be estimated or obtained from areference melting temperature (T_(m) ⁰) using the formula:$\begin{matrix}{\frac{1}{T_{m}} = {\frac{1}{T_{m}^{0}} + {k \times \ln \frac{\lbrack X^{+} \rbrack}{\lbrack X^{+} \rbrack_{0}}}}} & ( {{Equation}\quad 5.1} )\end{matrix}$

[0058] In the present invention, the coefficient k is preferably afunction of the polynucleotide's G-C content value; i.e., of ƒ(G-C). Itis noted that for Equations such as Equation 5.1, as well as for otherequations throughout the specification based on the reciprocal of themelting temperature (i.e., 1/T_(m)) temperatures should be entered inunits of Kelvin. For equations provided in this application that involveT_(m) (for example, Equation 5.2) units of Kelvin and degrees Celsiusmay be used interchangeably. Those skilled in the art will be able toreadily convert between units of Kelvin and other scales for measuringtemperature (e.g. degrees Celsius) using formulas that are well knownand routinely used in the art (for example: K=° C. 30 273.15).

[0059] In many embodiments, the relationship provided in Equation 5.1,supra, may be well approximated by a linear function of the referencemelting temperature (T_(m) ⁰) rather than of its inverse (i.e., 1/T_(m)⁰). Such a relationship is less computationally intensive than Equation5.1, and therefore will be simpler to use. Accordingly, the use of sucha linear approximation may be preferred, particularly when consideringthe relatively narrow range of temperatures for which meltingtemperatures of nucleic acids are typically be considered; i.e., forphysiological temperatures, preferably between about 20 and 80° C.(i.e., between about 293 and 353 K).

[0060] Accordingly, in another preferred embodiment, a salt-correctedmelting temperature (T_(m)) may be estimated or obtained from areference melting temperature (T_(m) ⁰) using the formula:$\begin{matrix}{T_{m} = {T_{m}^{0} + {k^{\prime} \times \ln \frac{\lbrack X^{+} \rbrack}{\lbrack X^{+} \rbrack_{0}}}}} & ( {{Equation}\quad 5.2} )\end{matrix}$

[0061] which is a linear approximation of Equation 5.1, supra. Again,the coefficient k′ is preferably a function of the polynucleotide's G-Ccontent value; i.e., of ƒ(G-C).

[0062] The coefficient k (or k′) is preferably obtained or provided by aformula of the general form:

k=k(ƒ(G-C))=m·ƒ(G-C)+k ₀   (Equation 5.3)

[0063] In this equation, m and k₀ are constant coefficients which may beoptimized to determine melting temperatures for polynucleotides havingdifferent G-C content under the salt concentration(s) or range of saltconcentrations of interest. For instance, the examples infra describeexperiments when appropriate values for these coefficients are optimizedfor both of Equation 5.1 and 5.2 above, by optimizing the fit quality tomelting data for a plurality of polynucleotide sequences. Those skilledin the art will appreciate that the exact value of the coefficients mand k₀ will depend on which formula (Equation 5.1 or 5.2) is used toestimate or obtain the salt-corrected melting temperature. Therefore,the coefficients are preferably optimized independently for eachformula.

[0064] Formulas for estimating or providing a salt-corrected meltingtemperature (e.g., Equations 5.1 and 5.2, above) may be furtheroptimized by the addition of one or more higher order polynomial term.For example, and not by way of limitation, Equation 5.1 above may bereadily modified by the addition of a second order polynomial term, toobtain a formula such as: $\begin{matrix}{\frac{1}{T_{m}} = {\frac{1}{T_{m}^{0}} + {k \times \ln \frac{\lbrack X^{+} \rbrack}{\lbrack X^{+} \rbrack_{0}}} + {b \times ( {{\ln^{2}\lbrack X^{+} \rbrack} - {\ln^{2}\lbrack X^{+} \rbrack}_{0}} )}}} & ( {{Equation}\quad 5.4} )\end{matrix}$

[0065] As before, the coefficient k is preferably a function of thepolynucleotide's G-C content value that is optimized for evaluatingmelting temperatures at the particular salt concentration(s) ofinterest. As described, supra, (e.g., for Equations 5.1 and 5.2), thecoefficient k is preferably obtained or provided by a formula of thegeneral form:

k=k(ƒ(G-C))=m·ƒ(G-C)+k ₀   (Equation 5.3)

[0066] where, again, the coefficients m and k₀ may be optimized todetermine melting temperatures for polynucleotides under the saltconcentration(s) or range of salt concentrations of interest. Again, theexact value of these coefficients should depend on which formula is usedto estimate the salt-corrected melting temperature; i.e., thecoefficients are preferably optimized independently for each formula.

[0067] As another example, Equation 5.2 above may also be readilymodified by the addition of a second order polynomial term, to obtain aformula such as: $\begin{matrix}{T_{m} = {T_{m}^{0} + {k \times \ln \frac{\lbrack X^{+} \rbrack}{\lbrack X^{+} \rbrack_{0}}} + {b \times ( {{\ln^{2}\lbrack X^{+} \rbrack} - {\ln^{2}\lbrack X^{+} \rbrack}_{0}} )}}} & ( {{Equation}\quad 5.5} )\end{matrix}$

[0068] As with the other formulas, the coefficient k is preferably afunction of the polynucleotide's G-C content value that is optimized forevaluating melting temperatures at the particular salt concentration(s)or range of salt concentrations of interest; for example, by optimizingthe coefficient m and k₀ in Equation 5.3, supra. Again, the coefficientsare preferably optimized for each formula described in this application.

[0069] Equations such as Equation 5.1-5.2 and 5.4-5.5 above may be stillfurther refined by adding additional polynominal terms; e.g., beyond thesecond order polynomial terms exemplified in Equations 5.4 and 5.5.Thus, for example, embodiments of the invention are also contemplatedthat may use, e.g., a third order, forth order, and/or even a fifthorder polynomial term. Those skilled in the art will be able to modifythe equations used in this invention to incorporate still higher orderpolynomial terms; e.g., using routine formulas and methods well known inthe mathematical arts.

[0070] Implementation Systems and Methods:

[0071] Computer System. The analytical methods described herein can beimplemented by the use of one or more computer systems. FIG. 2schematically illustrates an exemplary computer system suitable forimplementation of the analytical methods of this invention. Thecomponents of the computer system 201 include processor element 202interconnected with a main memory 203. The computer system can othercomponents such as a mass storage device 204 and user interface devices205 including for example, example, a monitor, a keyboard, and/orpointing devices 206 like a mouse or other graphical input device. Thecomputer system 201 can be linked to a network 207, which can be part ofan Ethernet, a local computer system (e.g., as part of a local areanetwork or LAN), and/or a wide area communication network (WAN) such asthe Internet.

[0072] Typically, one or more software components are loaded into mainmemory 203 during operation of computer system 201. Software component210 represents an operating system, which is responsible for managingcomputer system 201 and its network connections. Software component 211represents common languages and functions in the system to assistprograms implementing the methods specific to the invention. Equationsfor practicing the methods of the invention can also be programmed andimplemented using any programmable spread sheet software program.Programmable database systems (for example, a SQL database) can be usedto program and/or implement the equations and methods of this invention.Thus, software component 212 represents the analytic methods of theinvention as programmed in an appropriate procedural language, symbolicpackage, or the like.

[0073] Computer Program Products. The invention also provides computerprogram products which can be used, e.g., to program or configure acomputer system for implementation of analytical methods of theinvention. A computer program product of the invention comprises acomputer readable medium such as one or more compact disks (i.e., one ormore “CDs”, which may be CD-ROMs or a RW-CDs), one or more DVDs, one ormore floppy disks (including, for example, one or more ZIP™ disks) orone or more DATs to name a few. The computer readable medium has encodedthereon, in computer readable form, one or more of the softwarecomponents 212 that, when loaded into memory 203 of a computer system201, cause the computer system to implement analytic methods of theinvention. The computer readable medium may also have other softwarecomponents encoded thereon in computer readable form. Such othersoftware components may include, for example, functional languages 211or an operating system 210.

[0074] System Implementation. In an exemplary implementation, topractice the methods of the invention a G-C content value and/or cationconcentration may be loaded into the computer system 201. For example,the G-C content value may be directly entered by a user from monitor andkeyboard 205 by directly typing a sequence of symbols representingnumbers (e.g., G-C content value). Alternatively, a user may specify areference ion concentration, e.g., by selecting an ion concentrationfrom a menu of candidate ion concentrations presented on the monitor orby entering an accession number for a ion concentration in a databaseand the computer system may access the selected ion concentration fromthe database, e.g., by accessing a database in memory 203 or byaccessing the sequence from a database over the network connection,e.g., over the internet.

[0075] Finally, the software components of the computer system, whenloaded into memory 203, preferably also cause the computer system toestimate a melting temperature according to the methods describedherein. For example, the software components may cause the computersystem to obtain a reference melting temperature at a particularreference ion concentration for the polynucleotide and then use thereference melting temperature to calculate a modified meltingtemperature for the polynucleotide utilizing the methods describedherein.

[0076] Upon implementing these analytic methods, the computer systempreferably then outputs, e.g., the melting temperature for thepolynucleotide at a desired ion concentration. The output may be outputto the monitor, printed on a printer (not shown), written on massstorage 204 or sent through a computer network (e.g., the internet or anintranet such as a Local Area Network) to one or more other computers.

[0077] Alternative systems and methods for implementing the analyticmethods of this invention are also intended to be comprehended withinthe accompanying claims. In particular, the accompanying claims areintended to include the alternative program structures for implementingthe methods of this invention that will be readily apparent to thoseskilled in the relevant art(s).

EXAMPLES

[0078] The present invention is also described by means of the followingexamples. However, the use of these or other examples anywhere in thespecification is illustrative only and in no way limits the scope andmeaning of the invention or of any exemplified term. Likewise, theinvention is not limited to any particular preferred embodimentsdescribed herein. Indeed, many modifications and variations of theinvention may be apparent to those skilled in the art upon reading thisspecification and can be made without departing from its spirit andscope. The invention is therefore to be limited only by the terms of theappended claims along with the full scope of equivalents to which theclaims are entitled.

Example 1

[0079] Melting Temperatures of Various Oligomers Measured in DifferentSalt Conditions:

[0080] This example describes experiments in which melting profiles weremeasured for at least 92 different, exemplary oligonucleotide moleculesin various salt concentrations. Melting temperatures are extracted fromthose profiles for each oligonucleotide at each salt concentrationobserved, and those melting temperatures are provided in the results,infra. Sequence information for each of the exemplary oligonucleotidesis also provided.

[0081] Materials and Methods

[0082] Oligonucleotide synthesis and purification. DNA oligonucleotides(SEQ ID NOS:1-92) were synthesized using solid phase phosphoramiditechemistry, deprotected and desalted on NAP-5 columns (Amersham PharmaciaBiotech, Piscataway, N.J.) according to routine techniques (Caruthers etal., Methods Enzymol. 1992, 211:3-20). The oligomers were purified using20% polyacrylamide gel electrophoresis in 1×TBE buffer (50 mM Tris, 50mM boric acid, 1 mM Na₂EDTA). The purity of each oligomer was determinedby capillary electrophoresis (CE) carried out on a Beckman PACE 5000(Beckman Coulter, Inc., Fullerton, Calif.). The CE capillaries had a 100μm inner diameter and contained ssDNA 100R Gel (Beckman-Coulter).Typically, about 0.6 nmole of oligonucleotide was injected into acapillary, ran in an electric field of 444 V/cm and detected by UVabsorbance at 260 nm. Denaturing Tris-Borate-7 M-urea running buffer waspurchased from Beckman-Coulter.

[0083] Compound identity was verified by matrix-assisted laserdesorption ionization time-of-light (MALDI-TOF) mass spectroscopy on aVoyager DE™ Biospectometry™ Work station (Applied Biosystems, Foster,Calif.) following the manufacturer's recommended protocol.

[0084] Preparation of DNA samples. Melting experiments were carried outin buffer containing 3.87 mM NaH₂PO₄, 6.13 mM Na₂HPO₄, 1 mM Na₂EDTA andeither 50, 100, 200, 600 or 1000 mM NaCl. 1 M NaOH was used to titrateeach solution to pH 7.0. Total sodium concentrations were 68.9, 119,220, 621 and 1020 mM.

[0085] The DNA samples were thoroughly dialyzed against melting bufferin a 28-Well Microdialysis System (Invitation Corp., Carlsbad, Calif.)following the manufacturer's recommended protocol. Concentrations of DNAoligomers were estimated from the samples' UV absorbance at 260 nm in aspectrophotometer (Beckman Coulter, Inc., Fullerton, Calif.), usingextinction coefficients for each oligonucleotide that were estimatedusing the nearest neighbor model for calculating extinctioncoefficients. (See, Warshaw et al., J. Mol. Biol. 1966, 20:29-38;

[0086] See also,http://www.idtdna.com/program/techbulletins/calculating_Molar_Extinction_Coefficient.asp).Oligomer concentrations were estimated at least twice for each sample.If the estimated concentrations for any sample differed more than 4%,the results were discarded and new absorbance measurements wereperformed.

[0087] To prepare oligonucleotide duplexes, complementary DNA oligomerswere mixed in 1:1 molar ratio, heated to 367 K (i.e., 94° C.) and slowlycooled to an ambient temperature. Each solution of duplex DNA wasdiluted with melting buffer to a total DNA concentration (C_(T)) of 2μM.

[0088] Measurement of melting curves. Melting experiments were conductedon a single beam Beckman DU 650 spectrophotometer (Beckman-Coulter) witha Micro T_(m) Analysis accessory, a Beckman High Performance PeltierController (to regulate the temperature), and either 1 cm or 1 mmpath-length cuvettes. Melt data were recorded using a PC interfaced tothe spectrophotometer. UV-absorbance values at 268 nm wavelength weremeasured at 0.1 degree increments in the temperature range from 383 to368 K (i.e., 10-95° C.). Both heating (i.e., “denaturation”) and cooling(i.e., “renaturation”) transition curves were recorded in each sample ata controlled rate of temperature change (24.9±0.3 Kelvin per hour).Sample temperatures were collected from the internal probe locatedinside the Peltier holder, and recorded with each sample's UV-absorbancedata. Melting profiles were also recorded for samples of buffer alone(no oligonucleotide), and these “blank” profiles were digitallysubtracted from melting curves of the DNA samples. To minimizesystematic errors, at least two melting curves were collected for eachsample in different cuvettes and in different positions within thePeltier holder. Determination of melting temperatures. To determine eachsample's melting temperature, the melting profiles were analyzed usingmethods that have been previously described (see, Doktycz et al.,Biopolymers 1992, 32:849-864; Owczarzy et al., Biopolymers 1997,44:217-239). Briefly, the experimental data for each sample wassmoothed, using a digital filter, to obtain a plot of the sample'sUV-absorbance as a function of its temperature. The fraction ofsingle-stranded oligonucleotide molecules, θ, was then calculated fromthat plot. The “melting temperature” or “T_(m)” of a sample was definedas the temperature where θ=0.5.

[0089] Results:

[0090] To evaluate the effects of changing salt concentration on anoligonucleotide's melting temperature (T_(m)), a plurality of differentoligonucleotide molecules (also referred to as “oligomers”) weresynthesized and melting profiles were obtained for each oligomer underdifferent salt conditions. The term “melting profile” refers to acollection of measurements of an oligonucleotide and its complementwhich indicate the oligonucleotide molecule's transition fromdouble-stranded to single-stranded nucleic acid (or vice-versa). Thetransition of a nucleic acid from double-stranded to single-stranded isoften described in the art as the “melting” of that nucleic acidmolecule. The transition may also be described as the “denaturation” or“dissociation” of the nucleic acid. Accordingly, a melting profile ofthe present invention may also be referred to as a “dissociationprofile”, a “denaturation profile”, a “melting curve”, a “dissociationcurve”, etc.

[0091] It is well known in the art that a sample of double-strandednucleic acid molecules will absorb less UV-light than an equivalentsample of single-stranded nucleic acid molecules. Thus, in one preferredembodiment a melting profile may comprise a collection of measurementsindicating the UV absorption of a nucleic acid sample over a range oftemperatures. Such a collection of measurements was obtained for themelting profiles in this Example, following the procedures described inSection 6.1.1, supra. In such a melting profile, an increase inUV-absorption as the temperature increases will indicate the extent towhich more and more base pairs of duplex nucleic acid molecules in thesample are dissociating and an increasing fraction, θ, of thosemolecules are present in a single-stranded conformation. Conversely, adecrease in UV-absorption as the temperature decreases indicates thatmore and more base pairs are forming in the sample so that the fractionof double stranded nucleic acid molecules (1−θ) in the sample isincreasing while the fraction of single-stranded nucleic acid molecules(θ) is decreasing.

[0092] The “melting temperature” or “T_(m)” of a nucleic acid moleculerefers to the temperature above which the nucleic acid may generally beregarded as existing in a single-stranded conformation and below whichthe nucleic acid may generally be regarded as existing in adouble-stranded confirmation. It is well appreciated in the art that thetransition from double-stranded to single-stranded nucleic acidmolecules does not occur at a single temperature but, rather, occursover a range of temperatures (e.g., typically a range between about 5and 15° C.). Nevertheless, the T_(m) provides a convenient measurementfor approximating whether nucleic acid molecule in a sample exist in asingle-stranded or double-stranded conformation.

[0093] As an example, FIG. 1A shows an exemplary “UV-melting curve” fora 2 μM solution of the oligonucleotide 5′-TAACCATACTGAATACCTTTTGACG-3′(SEQ ID NO:45) and its complement dissolved in 68.9 mM Na⁺ buffer. This“melting curve” was obtained as described in the Material and Methodsection, supra. Because the solution absorbs more UV-light (260 nm) whenthe nucleic acid molecules are in a single-stranded conformation thenwhen they are in a double-stranded conformation, the UV-melting curve inFIG. 1A actually monitors the oligonucleotide's transition from thedouble-stranded to the single-stranded conformation. Inspection of theUV-melting curve reveals that the transition from double tosingle-stranded conformation does not occur completely at a singletemperature, but rather takes place across a range of temperatures.However, this range is very narrow (e.g., between about 5-15° C.). Thus,at temperatures above the center of this transition (e.g., above about56.5° C. or 329.7 K) the oligonucleotides in this sample can generallybe regarded as existing in a single-stranded conformation, whereas attemperatures below that “melting temperature” the oligonucleotides inthe sample are generally regarded as existing in a double-strandedconformation (i.e., as “duplex” oligonucleotide).

[0094]FIG. 1B shows data from a differential scanning calorimetry (DSC)experiment for a sample of the same oligonucleotide at much higherconcentrations (90 μM solution of SEQ ID NO: 45, C_(t)=180 μM, in 68.9mM Na⁺ buffer). For a detailed description of this experimentaltechnique, see, e.g., Cooper, Curr. Opinion Chem. Biol., 1999,3:557-563; and Plum & Breslauer, Curr. Opinion Struct. Biol., 1995,5:682-690.

[0095] The plot in FIG. 1B shows the sample's excess heat capacity(ΔC_(p)) as the temperature is raised from about 293 to about 363 K(i.e., 20 ° C. to about 90° C.). Heat capacity of the sample increasesas the oligonucleotide duplexes in that sample undergo a transition fromthe double-stranded conformation to the single-stranded conformation.Again, inspection of this figure shows that the transition occurs acrossa finite but narrow range (e.g., about 5-15 degrees) of temperaturescentered at approximately 63° C., where the heat absorption is maximal.Thus, again, at temperatures above about 63° C. (336 K) theoligonucleotides within this sample can generally be regarded asexisting in a single-stranded conformation, whereas the oligonucleotidesmay be generally regarded as existing in a double-stranded conformationat temperatures below about 63° C.

[0096] The observation that this transition (from double-stranded tosingle-stranded DNA) occurs at a higher temperature for the sample inFIG. 1B (approximately 63° C.) than for the sample in FIG. 1A (56.5° C.)may be readily attributed to the higher oligonucleotide concentration inFIG. 1B (180 μM vs. 2 μM) which, as is well known in the art, drives theequilibrium towards the double-stranded nucleic acid conformation.

[0097] Generally, the T_(m) of a nucleic acid may be defined as thetemperature at which one-half of the Watson-Crick base pairs in thedouble-stranded nucleic acid molecules are broken or dissociated (i.e.,they are “melted”) while the other half of the Watson-Crick base pairsremains intact; i.e., the fraction of broken base pairs, θ(T)=0.5 whenT=T_(m). However, in many cases the transition of oligonucleotides andother nucleic acids considered in this invention is or may be consideredas a “two-state” process in which an individual nucleic acid moleculeexists either as a duplex nucleic acid with all of its base-pairsintact, or as a single-stranded nucleic acid with no Watson-Crick basepairs between it and its complementary sequence. The fraction ofmolecules at any given temperature that are partially melted isnegligibly small. Accordingly, the fraction θ(T) may be considered asthe fraction of single-stranded nucleic acid molecules in a sample ofinterest, and 1−θ(T) is considered as the fraction of double-strandednucleic acid molecules in that sample. In such embodiments, the T_(m)may be equivalently defined as the temperature at which one-half of thenucleic acid molecules are in a single-stranded conformation andone-half of the nucleic acid molecules are in a double-strandedconformation. The exemplary melting and DSC curves shown in FIGS. 1A and1B, respectively, show that the transition of that oligonucleotide (SEQID NO:45) is a two-state process, with only a single transition betweentwo conformation states: double-stranded and single-stranded DNA. TheT_(m) is the temperature at the midpoint of that transition. Thus, themelting temperature of a nucleic acid sample may be readily obtained byevaluating a melting profile for that sample, such as the UV-meltingcurve illustrated in FIG. 1A or the DSC curve shown in FIG. 1B. See,also, the Materials and Methods Section, supra.

[0098] Oligonucleotides corresponding to each of the sequences set forthin SEQ ID NOS:1-92 and their complementary sequences were synthesizedand purified according to the methods described in the Materials andMethods section, supra. Capillary electrophoresis assays confirmed thatall samples were more than 90% pure, and experimental molar masses ofeach oligomer were confirmed within 0.4% of their predicted molar massby mass spectroscopy. For the melting experiments, each of theoligonucleotides listed in Table 1, below (SEQ ID NOS: 1-92) was mixedin a 1:1 molar ratio with its 100% complementary sequence, as describedin Material and Methods Section, supra. Melting profiles were thenrecorded for each oligomer in 68.9, 119, 220, 621 and 1020 mM Na⁺, andthe melting temperature extracted from each profile. The experimentallydetermined T_(m) values for each sample were reproducible within 0.3 C.

[0099] The T_(m) values obtained for each oligomer are provided in TableI, below. For convenience, the melting temperatures specified in Table Iare listed in units of Kelvin (K), which are preferably used in theimplementation of this invention. However, those skilled in the art willbe able to readily convert between units of Kelvin and other scales orunits for measuring temperature (e.g., degrees Celsius) using formulasthat are well known and routinely used in the art (for examples K=°C.+273.15). Sequence information was also recorded for each oligomer,including the total number of bases (N) and the G-C content.Specifically, an oligomer's G-C content ƒ(G-C) is defined here as thefraction of bases that are either guanine or cytosine. Thus, forexample, the oligonucleotide set forth in SEQ ID NO:1 comprises a totalof 15 bases pairs (i.e., N=15), of which three are either guanine orcytosine. Thus, that particular oligomer's G-C content may be obtainedor provided by: ƒ(G-C)={fraction (3/15)}=0.2. The nucleotide sequence,total number of base pairs and G-C content for each oligomer are alsoprovided in Table I, along with the corresponding SEQ ID NO. TABLE IMEASURED MELTING TEMPERATURES AT VARIOUS [Na⁺] CONCENTRATIONS T_(m) (K)SEQ ID (Total Na⁺ Concentration) NO. Sequence N ƒ(G-C) 68.9 mM 119 mM220 mM 621 mM 1020 mM 1 TACTAACATTAACTA 15 0.20 308.5 313.7 317.3 322.5324.3 2 ATACTTACTGATTAG 15 0.27 311.3 314.7 318.2 323.1 324.7 3GTACACTGTCTTATA 15 0.33 314.2 318.0 321.5 326.1 328.0 4 GTATGAGAGACTTTA15 0.33 313.1 317.4 321.1 326.5 328.6 5 TTCTACCTATGTGAT 15 0.33 313.8317.8 321.3 325.4 326.9 6 AGTAGTAATCACACC 15 0.40 317.5 321.0 324.8329.4 330.3 7 ATCGTCTCGGTATAA 15 0.40 318.7 322.6 326.1 330.6 331.8 8ACGACAGGTTTACCA 15 0.47 321.0 324.4 328.7 333.0 334.5 9 CTTTCATGTCCGCAT15 0.47 323.2 327.1 330.3 334.6 335.9 10 TGGATGTGTGAACAC 15 0.47 319.7324.8 327.8 332.3 333.5 11 ACCCCGCAATACATG 15 0.53 324.52 328.5 331.7335.6 336.1 12 GCAGTGGATGTGAGA 15 0.53 324.4 328.0 331.2 334.9 336.5 13GGTCCTTACTTGGTG 15 0.53 321.0 324.8 328.3 332.3 333.5 14 CGCCTCATGCTCATC15 0.60 326.0 329.9 333.3 336.8 339.0 15 AAATAGCCGGGCCGC 15 0.67 332.2335.4 338.5 342.2 343.6 16 CCAGCCAGTCTCTCC 15 0.67 327.3 331.2 334.7338.3 339.9 17 GACGACAAGACCGCG 15 0.67 331.1 334.7 337.6 340.8 341.8 18CAGCCTCGTCGCAGC 15 0.73 334.0 337.3 340.6 343.3 345.2 19 CTCGCGGTCGAAGCG15 0.73 334.7 337.8 340.3 343.2 343.9 20 GCGTCGGTCCGGGCT 15 0.80 338.1340.9 343.7 347.1 347.3 21 TATGTATATTTTGTAATCAG 20 0.20 317.6 320.9325.7 330.8 334.4 22 TTCAAGTTAAACATTCTATC 20 0.25 318.9 322.7 327.1332.6 334.7 23 TGATTCTACCTATGTGATTT 20 0.30 322.3 326.7 330.6 335.5337.6 24 GAGATTGTTTCCCTTTCAAA 20 0.35 322.5 326.0 330.8 335.8 338.5 25ATGCAATGCTACATATTCGC 20 0.40 328.4 332.7 336.1 340.2 342.1 26CCACTATACCATCTATGTAC 20 0.40 324.3 327.8 331.6 335.4 337.6 27CCATCATTGTGTCTACCTCA 20 0.45 328.8 332.7 336.4 340.5 341.7 28CGGGACCAACTAAAGGAAAT 20 0.45 326.9 331.0 334.9 339.9 341.7 29TAGTGGCGATTAGATTCTGC 20 0.45 330.2 333.8 338.0 342.4 344.4 30AGCTGCAGTGGATGTGAGAA 20 0.50 332.9 336.7 340.8 344.5 346.3 31TACTTCCAGTGCTCAGCGTA 20 0.50 333.5 337.6 340.9 344.8 346.8 32CAGTGAGACAGCAATGGTCG 20 0.55 333.0 336.7 340.2 344.3 345.7 33CGAGCTTATCCCTATCCCTC 20 0.55 329.2 333.5 337.3 341.5 343.5 34CGTACTAGCGTTGGTCATGG 20 0.55 332.8 336.3 339.8 343.7 344.3 35AAGGCGAGTCAGGCTCAGTG 20 0.60 337.7 340.9 344.6 348.3 349.5 36ACCGACGACGCTGATCCGAT 20 0.60 339.2 342.3 345.8 350.0 350.5 37AGCAGTCCGCCACACCCTGA 20 0.65 339.7 343.1 347.2 350.1 351.7 38CAGCCTCGTTCGCACAGCCC 20 0.70 340.4 343.9 347.2 350.9 351.4 39GTGGTGGGCCGTGCGCTCTG 20 0.75 342.4 345.9 349.4 352.8 354.2 40GTCCACGCCCGGTGCGACGG 20 0.80 344.1 347.1 350.5 353.0 354.3 41GATATAGCAAAATTCTAAGTTAATA 25 0.20 322.3 326.7 330.9 336.5 339.4 42ATAACTTFACGTGTGTGACCTATTA 25 0.32 329.8 333.9 337.9 342.8 345.0 43GITCTATACTCTTGAAGTTGATTAC 25 0.32 325.9 329.3 333.8 339.3 340.9 44CCCTGCACTTTAACTGAATTGTTTA 25 0.36 330.7 334.6 338.8 343.3 345.7 45TAACCATACTGAATACCTTTTGACG 25 0.36 329.7 333.4 337.5 342.1 344.5 46TCCACACGGTAGTAAAATTAGGCTT 25 0.40 332.5 336.3 340.5 345.0 347.0 47TTCCAAAAGGAGTTATGAGTTGCGA 25 0.40 332.3 336.2 340.4 344.8 347.0 48AATATCTCTCATGCGCCAAGCTACA 25 0.44 335.3 338.9 343.5 348.2 349.7 49TAGTATATCGCAGCATCATACAGGC 25 0.44 334.4 337.9 342.3 346.0 348.2 50TGGATTCTACTCAACCTTAGTCTGG 25 0.44 332.2 336.3 340.3 344.5 346.8 51CGGAATCCATGTTACTTCGGCTATC 25 0.48 333.9 337.9 341.9 346.5 347.9 52CTGGTCTGGATCTGAGAACTTCAGG 25 0.52 335.3 339.0 342.8 347.4 348.8 53ACAGCGAATGGACCTACGTGGCCTT 25 0.56 341.3 345.3 349.2 352.6 354.3 54AGCAAGTCGAGCAGGGCCTACGTTT 25 0.56 341.5 345.8 349.5 353.2 354.7 55GCGAGCGACAGGTTACTTGGCTGAT 25 0.56 340.2 344.0 347.9 351.8 353.3 56AAAGGTGTCGCGOAGAGTCGTGCTG 25 0.60 342.8 346.8 350.6 354.4 355.6 57ATGGGTGGGAGCCTCGGTAGCAGCC 25 0.68 343.9 347.7 351.4 354.8 356.6 58CAGTGGGCTCCTGGGCGTGCTGGTC 25 0.72 345.1 348.8 352.3 355.8 356.5 59GCCAACTCCGTCGCCGTTCGTGCGC 25 0.72 346.8 349.6 353.8 356.4 357.8 60ACGGGTCCCCGCACCGCACCGCCAG 25 0.80 350.0 353.1 357.2 360.3 361.5 61TTATGTATTAAGTTATATAGTAGTAGTAGT 30 0.20 323.9 328.2 332.5 338.3 339.8 62ATTGATATCCTTTTCTATTCATCTTTCATT 30 0.23 326.7 331.5 335.5 341.8 343.6 63AAAGTACATCAACATAGAGAATTGCATTTC 30 0.30 331.5 335.1 339.3 344.5 346.4 64CTTAAOATATGAGAACTTCAACTAATGTGT 30 0.30 330.0 334.5 338.1 343.7 345.0 65CTCAACTTGCGGTAAATAAATCGCTTAATC 30 0.37 334.0 338.0 341.9 347.6 348.7 66TATTGAGAACAAGTGTCCGATTAGCAGAAA 30 0.37 334.5 338.6 342.8 348.0 349.6 67GTCATACGACTGAGTGCAACATTGTTCAAA 30 0.40 335.9 340.0 344.0 349.1 350.1 68AACCTGCAACATGGAGTTTTTGTCTCATGC 30 0.43 337.7 341.5 345.7 350.9 351.9 69CCGTGCGGTGTGTACGTTTTATTCATCATA 30 0.43 337.1 341.5 345.0 349.7 350.8 70GTTCACGTCCGAAAGCTCGAAAAAGGATAC 30 0.47 337.5 341.4 345.3 350.4 351.9 71AGTCTGGTCTGGATCTGAGAACTTCAGGCT 30 0.50 339.5 343.6 347.7 352.0 353.8 72TCGGAGAAATCACTGAGCTGCCTGAGAAGA 30 0.50 339.5 343.6 347.3 352.2 354.2 73CTTCAACGGATCAGGTAGGACTGTGGTGGG 30 0.57 340.8 344.9 347.9 352.1 353.3 74ACGCCCACAGGATTAGGCTGGCCCACATTG 30 0.60 344.5 347.9 351.7 355.9 357.2 75GTTATTCCGCAGTCCGATGGCAGCAGGCTC 30 0.60 343.8 348.1 351.3 355.6 357.3 76TCAGTAGGCGTGACGCAGAGCTGGCGATGG 30 0.63 345.4 348.9 352.5 356.5 357.8 77CGCGCCACGTGTGATCTACAGCCGTTCGGC 30 0.67 345.9 349.5 352.7 356.6 357.7 78GACCTGACGTGGACCGCTCCTGGGCGTGGT 30 0.70 347.7 351.6 354.7 358.4 359.5 79GCCCCTCCACTGGCCGACGGCAGCAGGCTC 30 0.77 349.5 353.0 356.8 360.3 360.9 80CGCCGCTGCCGACTGGAGGAGCGCGGGACG 30 0.80 351.0 354.8 357.8 360.9 361.8 81ATCAATCATA 10 0.20 294.5 297.7 301.1 305.6 306.8 82 TTGTAGTCAT 10 0.30297.8 301.0 304.4 308.0 309.2 83 GAAATGAAAG 10 0.30 295.3 298.5 302.3306.3 307.6 84 CCAACTTCTT 10 0.40 302.2 305.3 309.1 312.8 313.8 85ATCGTCTGGA 10 0.50 307.0 310.6 313.7 317.7 318.1 86 AGCGTAAGTC 10 0.50300.6 304.3 307.8 312.7 313.4 87 CGATCTGCGA 10 0.60 312.4 315.5 318.8321.6 322.3 88 TGGCGAGCAC 10 0.70 317.6 321.1 324.5 328.2 328.5 89GATGCGCTCG 10 0.70 317.4 320.2 323.3 326.8 326.7 90 GGGACCGCCT 10 0.80319.9 323.5 326.3 329.7 330.2 91 CGTACACATGC 11 0.55 313.5 316.7 319.3322.8 323.1 92 CCATTGCTACC 11 0.55 311.3 314.9 317.7 321.1 322.1

Example 2

[0100] Sequence Dependent Salt Effects on T_(m)

[0101] As an initial evaluation of the effect(s) sequence compositionand length may have on a nucleic acid's melting temperature T_(m), theexperimentally determined melting temperatures for each oligonucleotidein Table I, supra, were fit in a least squares analysis to each of thefollowing linear regressions:

T _(m) =T _(m) ⁰ +m log [Na⁺]  (Equation 6.1)

[0102] $\begin{matrix}{\frac{1}{T_{m}} = {\frac{1}{T_{m}^{0}} + {m\quad {\log \lbrack {Na}^{+} \rbrack}}}} & ( {{Equation}\quad 6.2} )\end{matrix}$

[0103] Equations that are similar in form to Equations 6.1 and 6.2 arewell known in the art and have been used to predict nucleic acid meltingtemperatures for specified salt concentrations. However, the versions ofthese formulas that have been previously described use coefficients(i.e., for m) that are constants and are independent of (and thereforeunaffected by) either the nucleic acid's length or base composition. Forexample, Schildraut et al. (Biopolymers 1965, 3:195-208) describe anequation that is similar to Equation 6.1, above, for estimating anucleic acid's melting temperature as a function of sodium ionconcentration:

T _(m)(Na⁺)=T _(m)(1M)+16.6 log [Na⁺]  (Equation 6.3)

[0104] See also, Rychlik et al., Nucl. Acids Res. 1990, 18:6409; Ivanov& AbouHaidar, Analytical Biochemistry 1995, 232:249-251; and Wetmur,Critical Review in Biochemistry and Molecular Biology 1991, 26:227-259.In the above Equation 6.3, the oligomer's melting temperature in 1 Msodium salt is used as the reference melting temperature (i.e., T_(m)⁰=T_(m)(1M) ). This reference temperature may be measured (e.g., asdescribed above) or it may be calculated or predicted, e.g., by thenearest neighbor model of Breslauer et al., Proc. Natl. Acad. Sci.U.S.A. 1986, 83:3746-3750. See also, SantaLucia et al., Biochemistry1996, 35:3555-3562; and Santa Lucia, Proc. Natl. Acad. Sci. U.S.A. 1998,95:1460-1465.

[0105] Others have used a formula that is similar to Equation 6.3,above, but using a value of m=12.5 rather than 16.6. (See, SantaLucia etal., Biochemistry 1996, 35:3555-3562).

[0106] Alternatively, an equation that relates the entropy change ofoligonucleotide dissociation, ΔS°, to changing sodium ion concentrationshas also been proposed (See, Santa Lucia, Proc. Natl. Acad. Sci U.S.A.,1998, 95:1460-1465):

ΔS° (Na⁺)=ΔS° (1M)+0.368Nln [Na⁺]  (Equation 6.4)

[0107] where N is the total number of phosphates in the nucleotideduplex divided by two and ΔS° (1M) is the entropy of dissociation in 1MNa⁺, which is preferably calculated using an appropriate nearestneighbor model (described above). Equations are also well known in theart that relate the melting temperature, T_(m), to the enthalpy andentropy of oligonucleotide dissociation (ΔH° and ΔS°, respectively) andthe total oligonucleotide strand concentration, C_(T) (for example, seeSanta Lucia, supra): $\begin{matrix}{T_{m} = \frac{\Delta \quad H^{0}}{( {{\Delta \quad S^{0}} + {R\quad \ln \quad {C_{T}/4}}} )}} & ( {{Equation}\quad 6.5} )\end{matrix}$

[0108] If it is assumed that the enthalpy of polynucleotide dissociationdoes not vary in changing salt conditions, then Equations 6.4 and 6.5above may be readily combined to derive an alternative equation relatingT_(m) to salt concentration: $\begin{matrix}{\frac{1}{T_{m}} = {\frac{1}{T_{m}^{0}} + {\frac{0.368\quad N}{\Delta \quad H^{0}} \times \ln \frac{\lbrack {Na}^{+} \rbrack}{\lbrack {Na}^{+} \rbrack_{0}}}}} & ( {{Equation}\quad 6.6} )\end{matrix}$

[0109] where standard transition enthalpy, ΔH°, is preferably calculatedusing an appropriate nearest neighbor model.

[0110] None of the equations described above accounts for any content ofthe particular polynucleotide sequence under consideration. Indeed,existing models of polynucleotide dissociation assume that cationsstabilize polynucleotide duplexes by partially neutralizing the negativecharges of each strand's phosphate background. (See, Schildkraut et al.,Biopolymers 1965, 3:195-208; and SantaLucia et al., Proc. Natl. Acad.Sci 1998, 95:1460-1465). Such models suggest that any salt effect onpolynucleotide dissociation would be sequence independent.

[0111] Applicants have determined, however, that the effect(s) of saltconcentration on the melting temperature of a nucleic acid is itselfdependent on the nucleotide sequence. This discovery is readily apparentfrom the preliminary analysis described in this example. A coefficientvalue m was obtained for each oligomer in Table I when its measuredmelting temperatures are fit to Equation 6.1. The coefficients m thusobtained for each oligonucleotide are plotted in FIG. 3, as a functionof the oligomer's G-C content ƒ(G-C). If the effects of changing saltconcentration on the melting temperature were in fact sequenceindependent, as suggested by the prior art and by Equation 6.3, the samecoefficient m would be obtained for all oligomers and the data plottedin FIG. 3 would form a horizontal line. However, it is apparent frominspection of FIG. 3 that the coefficient in actually decreases as theG-C content increases.

[0112] Data points for oligomers of 15, 20, 25 and 30 base pairs inlength are distinctly labeled in FIG. 3. The coefficient m decreases ata similar rate for oligomers of all these different lengths. Thus, thesedata demonstrate that while the effect of changing salt concentrationdepends upon the sequence composition of a nucleic acid, it issubstantially independent of the nucleic acid's length.

[0113]FIG. 4 shows, as a function of the G-C content ƒ(G-C), thecoefficient m obtained for each oligomer in Table II when its measuredmelting temperatures are fit to Equation 6.2, supra. Again, if theeffects of changing salt concentration on melting temperature wereactually sequence independent (as suggested by formulas used in theprior art) the data plotted in this figure would form a horizontal line.In fact, however, the coefficient m increases linearly with theoligomers' G-C content. As in FIG. 3, the coefficient m changes at asimilar rate with G-C content for oligomers of different length. Thus,FIG. 4 also demonstrates that, while the effect of changing saltconcentration depends upon the sequence composition of a nucleic acid,the effect is substantially independent of the nucleic acid's length.

Example 3

[0114] Formulas for Improved Prediction of T_(m) for Different SaltConditions

[0115] To evaluate the effect(s) that differing salt concentrations mayhave on an oligonucleotide's melting temperature, the experimentallydetermined melting temperatures set forth in Table I, supra, were fit tovarious different equations that predict melting temperature based on:(1) salt concentration (in this example, [Na⁺]), and (2) oligonucleotidesequence content (e.g., ƒ(G-C)). Generally speaking, the equations wereof one of the following forms: $\begin{matrix}{T_{m} = {T_{m}^{0} + {{k( {f( {G - C} )} )} \times \ln \frac{\lbrack {Na}^{+} \rbrack}{\lbrack {Na}^{+} \rbrack_{0}}} + {b \times ( {{\ln^{2}\lbrack {Na}^{+} \rbrack}_{(1)} - {\ln^{2}\lbrack {Na}^{+} \rbrack}_{(0)}} )}}} & ( {{Equation}\quad 6.7} ) \\{\frac{1}{T_{m}} = {\frac{1}{T_{m}^{0}} + {k( {f( {G - C} )} ) \times \ln \frac{\lbrack {Na}^{+} \rbrack}{\lbrack {Na}^{+} \rbrack_{0}}} + {b \times ( {{\ln^{2}\lbrack {Na}^{+} \rbrack} - {\ln^{2}\lbrack {Na}^{+} \rbrack}_{(0)}} )}}} & ( {{Equation}\quad 6.8} )\end{matrix}$

[0116] In Equations 6.7 and 6.8, above, T_(m) denotes a meltingtemperature to be determined for a nucleic acid in a particularconcentration of monovalent cations, [Na⁺]. T_(m) ⁰ denotes the nucleicacid's melting temperature in some “reference” concentration of themonovalent cations [Na⁺]₍₀₎. Typically, a value of 1 M is selected asthe reference concentration (i.e., [Na⁺]_((o))=1 M). However, any valuemay be selected for a reference concentration and a skilled artisanpracticing this invention will readily appreciate when and what otherreference concentration values may be used.

[0117] The reference melting temperature, T_(m) ⁰ may be a meltingtemperature that is experimentally determined (e.g., as described inSection 6.1, above) for the nucleic acid at the reference concentrationof cations, [Na⁺]₍₀₎. However, the value of T_(m) ⁰ may also becalculated using methods, such as the nearest neighbor model, that arewell known and routinely used in the art to determine a nucleic acid'smelting temperature at some concentration of cations. For instance, thereference melting temperature T_(m) ⁰ may be calculated using a nearestneighbor model as described, e.g., by SantaLucia et al., Proc. Natl.Acad. Sci. U.S.A. 1998, 95:1460; or, less preferably, Breslauer et al.,Proc. Natl. Acad. Sci. U.S.A. 1986, 83:3746-3750 (see also, thereferences cited supra in connection with the nearest neighbor model).Preferably, both the predicted melting temperature T_(m), and thereference melting temperature T_(m) ⁰ are specified in Kelvin (K).

[0118] In embodiments where a reference melting temperature iscalculated from a theoretical model, the parameters of that model willtypically have been calibrated, optimized or otherwise selected for aparticular concentration of cations (e.g., for 1 M Na⁺). A skilledartisan practicing the invention will appreciate, therefore, that thereference concentration of cations used in such embodiments (i.e. thevalue (Na⁺]₍₀₎ in Equations 6.7 and 6.8, supra) will preferably be thatvalue for which the theoretical model's parameters have been evaluated.

[0119] In the present example and in most preferred embodiments of theinvention, the monovalent cations are sodium cations. However, use ofthe symbol for sodium cations (i.e., Na⁺) in the above equations is donehere merely to simplify the description of this invention. The formulaspresented here, as well as the algorithms they represent and illustrate,may be used to estimate or predict melting temperature in differentconcentrations of any monovalent cation, including lithium cations(Li⁺), potassium cations (K⁺), rubidium cations (Rb⁺), cesium cations(Cs⁺) and francium cations (Fr⁺) to name a few.

[0120] As demonstrated in Example 2, above, the effect of saltconcentration on the melting temperature of a nucleic acid is itselfdependent on nucleotide sequence. Moreover, Applicants have determined,as demonstrated here, that such sequence-dependent effects may beaccounted for when predicting or estimating T_(m) values, by simplyusing a coefficient k which is a function of the nucleotide sequencecontent. In particular and in preferred embodiments of the invention,the coefficient k may be a function of the nucleic acid's G-C contentƒ(G-C).

[0121] As used herein to describe the present invention, the G-C contentof a nucleic acid, ƒ(G-C), refers to the fraction of that nucleic acid'snucleotide bases that are either guanine (G) or cytosine (C). Thus, forexample, the oligomer set forth in SEQ ID NO:1 (see, also, in Table I,supra) comprises a total of 15 bases (i.e., n=15), of which three areeither guanine or cytosine. Thus, that oligomer's G-C content may beobtained or provided by: ƒ(G-C)={fraction (3/15)}=0.2.

[0122] The second term in Equations 6.7 and 6.8 (i.e., the term:b×(ln²[Na⁺]₍₁₎-ln²[Na⁺]₍₀₎)) is an exemplary second-order polynominalterm. In preferred embodiments, the use of this term with anappropriately selected coefficient value b provides for greater accuracyand greater reliability when estimating the melting temperature for anucleic acid under particular salt conditions.

[0123] In still other embodiments, additional higher order polynomialterms may also be used in Equations 6.7-6.8, to estimate salt-correctedmelting temperatures with even greater accuracy and reliability. Thus,the invention also contemplates the optional use of third, forth and/oreven fifth order polynomial terms. Those skilled in the art will be ableto modify the equations used in this invention to incorporate suchhigher order polynomial terms using routine formulas and methods wellknown in the mathematical arts.

[0124] Those skilled in the art will also recognize that, when higherorder polynominal terms are used in these equations, it will benecessary to re-optimize the coefficients for optimal results. Thus, forexample, when the second order polynominal term is used in Equation 6.7and/or 6.8 (i.e., b≠0) it may be necessary to select a value for thecoefficient k which, generally, will be different from the valueselected when such higher order polynominal terms are not used (i.e.,when b=0).

[0125] It is also noted that the formulas provided in Equations 6.7 and6.8 are set forth with respect to the “natural logarithm” (i.e., alogarithm of the base e=2.1718) of a cation concentration or of a ratioof cation concentrations. As a skilled user will readily appreciate, itmay be preferable in many instances to perform calculations usinglogarithms of a different base (e.g., the logarithm of base 10 or ofbase 2) which may, for example, be simpler to calculate. The logarithmicterms in Equations 6.7 and 6.8, as well as in the other formulas andequations set forth in this document, may be readily adapted to suchother forms by simply making an appropriate adjustment to thecoefficient(s); more specifically by multiplying the coefficient(s) byan appropriate factor. Those skilled in the art will be able to readilyobtain or determine the appropriate factor(s) and make the necessaryadjustment to the logarithmic coefficient(s). Accordingly, it isunderstood that versions of these equations which use logarithms ofother bases are mathematically equivalent to the equations andformulations set forth in this application, and merely providealternative representations or descriptions of the algorithms andcomputational methods of this invention. Indeed, those skilled in themathematical arts will appreciate that the equations and formulas setforth throughout this application may be written or expressed in avariety of different ways that are mathematically equivalent. Suchmathematically equivalent expressions merely represent alternativerepresentations or descriptions of the computational methods that theydescribe rather than any departure from those methods.

[0126] Values for the coefficients k and b were selected for Equations6.7 and 6.8, above, that optimized the fit of experimentally determinedT_(m) values (see, Table I, supra) to those equations. First, theexperimentally determined T_(m) values were fit to a form of thoseequations in which the optional second order polynominal term (i.e., theterm b×(ln²[Na⁺]₍₁₎−ln²[Na⁺]₍₀₎)) was omitted (i.e., b=0). A coefficientk was selected that is a linear function of the nucleic acid G-Ccontent:

k(ƒ(G-C))=m·ƒ(G-C)+k₀   (Equation 6.9)

[0127] Constant values for the coefficients m and k₀ were selected thatoptimized the goodness of fit. In a second analysis, the experimentallydetermined T_(m) values were fit to a form of Equations 6.7 and 6.8 thatincluded the optional second term (b≠0). The linear form of coefficientk set forth in Equation 6.9 was again used, and constant values for thecoefficients m, k₀ and b were selected to optimize goodness of fit.

[0128] In each analysis, a reference salt concentration of [Na⁺]₍₀₎=1.02M was used, and the reference melting temperature, T_(m) ⁽⁰⁾ was theoligomer's experimentally determined melting temperature at that cationconcentration. Goodness of fit was evaluated from the reduced“chi-square” value (X_(r) ²=X²/v) and from <|ΔT_(m)|>_(AVE), the averagedifference between the measured T_(m) values and corresponding T_(m)values predicted using the equation. The chi-squared goodness of fittest compares a theoretical distribution with the observed data from asample. (See William H. Press et al., Numerical Recipes in C. The Art ofScientific Computing 659-61 (2d Ed. 1992)). Thus, smaller values for(X_(r) ² and/or <|ΔT_(m)|>_(AVE) indicate that the equation or modelused accurately and reliably predicts actual melting temperatures fordifferent salt concentrations.

[0129] Coefficient values for each fit of the experimental data inEquations 6.7 and 6.8 are provided in Table II, below, along with eachfit's reduced chi-squared and <|ΔT_(m)|>_(AVE) values. TABLE IIEmpirical Fits of Experimental T_(m)Values Coefficient Equa- k = m · f(G− C) + k₀ Fit Quality tion m k₀ b χ²/v <|ΔT_(m)|>_(AVE) 6.8 4.29 × 10⁻⁵−3.95 × 10⁻⁵ 9.40 × 10⁻⁶ 4.4 0.5 6.7 −4.62 4.52 −0.985 9.9 0.7 6.8 3.85× 10⁻⁵ −6.18 × 10⁻⁵ - 0 - 19.5 1.1 6.7 −3.22 6.39 - 0 - 21.8 1.2

[0130] The date from Table I, supra, were also fit to Equations thathave been previously described for estimating salt effects onpolynucleotide melting temperatures. Each of those formulas is alsodiscussed herein above, in Example 2.

[0131] More specifically, the data in Table I were fit to a form ofEquation 6.1, supra using a coefficient m=16.6 (described by Schildkrautet al., Biopolmers 1965, 3:195-208) and also to a form of that equationwith the coefficients m=12.5 (See, SantaLucia et al., Biochemistry 1996,35:3555-3562). In addition, the data were also fit to Equation 6.6,supra.

[0132] As before, each analysis used a reference salt concentration[Na⁺]₍₀₎=1.02 M. The reference melting temperature, T_(m) ⁽⁰⁾ was theoligomer's experimentally determined melting temperature. The enthalpyterm in Equation 6.6 (i.e., ΔH°) was calculated for each oligonucleotideusing the nearest neighbor model and parameters optimized for 1 M Na⁺concentration (SantaLucia et al. Proc. Natl. Acad. Sci. 1998,95:1460-1465).

[0133] Goodness of fit was evaluated from the reduced “chi-square” value(X²=X²/v) and from <|ΔT_(m)|>_(AVE), the average difference between themeasured T_(m) values and corresponding T_(m) values predicted using theequation. The reduced chi-squared and <|ΔT_(m)|>_(AVE) values forEquations 6.1 and 6.6 are provided in Table III, below. TABLE IIIEMPIRICAL FITS OF EXPERIMENTAL T_(m) VALUES TO PRIOR ART EQUATIONSEquation χ²/v <|ΔT_(m)|>_(AVE) 6.6 44.3 1.7 6.1 (m = 16.6) 337.7 5.1 6.1(m = 12.5) 68.4 2.1

[0134] These results confirm that melting temperatures ofpolynucleotides may be more accurately and reliably estimated by usingformulas such as Equations 6.7 and 6.8, above, that depend on nucleotidecontent.

[0135] Thus, four new formulas are provided here which relate themelting temperature of a nucleic acid to the salt conditions in whichthe nucleic acid denaturation is actually performed: $\begin{matrix}{T_{m} = {T_{m}^{0} + {( {6.39 - {3.22 \times {f( {G - c} )}}} ) \times \ln \frac{\lbrack {Na}^{+} \rbrack}{\lbrack {Na}^{+} \rbrack_{0}}}}} & ( {{Equation}\quad 6.10} ) \\{\frac{1}{T_{m}} = {\frac{1}{T_{m}^{0}} + {( {{3.85 \times {f( {G - C} )}} - 6.18} ) \times 10^{- 5} \times \ln \frac{\lbrack {Na}^{+} \rbrack}{\lbrack {Na}^{+} \rbrack_{0}}}}} & ( {{Equation}\quad 6.11} ) \\{T_{m} = {T_{m}^{0} + {( {4.52 - {4.62 \times {f( {G - C} )}}} ) \times \ln \frac{\lbrack {Na}^{+} \rbrack}{\lbrack {Na}^{+} \rbrack_{0}}} - {0.985 \times \{ {{\ln^{2}\lbrack {Na}^{+} \rbrack} - {\ln^{2}\lbrack {Na}^{+} \rbrack}_{(0)}} \}}}} & ( {{Equation}\quad 6.12} ) \\{\frac{1}{T_{m}} = {\frac{1}{T_{m}^{0}} + {( {{4.29 \times {f( {G - C} )}} - 3.95} ) \times 10^{- 5} \times \ln \frac{\lbrack {Na}^{+} \rbrack}{\lbrack {Na}^{+} \rbrack_{0}}} + {9.40 \times 10^{- 6} \times \{ {{\ln^{2}\lbrack {Na}^{+} \rbrack} - {\ln^{2}\lbrack {Na}^{+} \rbrack}_{(0)}} \}}}} & ( {{Equation}\quad 6.13} )\end{matrix}$

[0136] Any one of these formulas may be used in connection with thepresent invention, e.g., to predict the melting temperature of aparticular nucleic acid in certain salt conditions. Indeed, the datapresented in Table II, and Table III supra, shows that these equationsand algorithms may predict or estimate the melting temperature of aparticular nucleic acid with greater accuracy and reliability thanexisting methods.

References Cited

[0137] Numerous references, including patents, patent applications andvarious publications, are cited and discussed in the description of thisinvention. The citation and/or discussion of such references is providedmerely to clarify the description of the present invention and is not anadmission that any such reference is “prior art” to the inventiondescribed herein. All references cited and discussed in thisspecification are incorporated herein by reference in their entirety andto the same extent as if each reference was individually incorporated byreference.

1 92 1 15 DNA Artificial Sequence oligonucleotide 1 tactaacatt aacta 152 15 DNA Artificial Sequence oligonucleotide 2 atacttactg attag 15 3 15DNA Artificial Sequence oligonucleotide 3 gtacactgtc ttata 15 4 15 DNAArtificial Sequence oligonucleotide 4 gtatgagaga cttta 15 5 15 DNAArtificial Sequence oligonucleotide 5 ttctacctat gtgat 15 6 15 DNAArtificial Sequence oligonucleotide 6 agtagtaatc acacc 15 7 15 DNAArtificial Sequence oligonucleotide 7 atcgtctcgg tataa 15 8 15 DNAArtificial Sequence oligonucleotide 8 acgacaggtt tacca 15 9 15 DNAArtificial Sequence oligonucleotide 9 ctttcatgtc cgcat 15 10 15 DNAArtificial Sequence oligonucleotide 10 tggatgtgtg aacac 15 11 15 DNAArtificial Sequence oligonucleotide 11 accccgcaat acatg 15 12 15 DNAArtificial Sequence oligonucleotide 12 gcagtggatg tgaga 15 13 15 DNAArtificial Sequence oligonucleotide 13 ggtccttact tggtg 15 14 15 DNAArtificial Sequence oligonucleotide 14 cgcctcatgc tcatc 15 15 15 DNAArtificial Sequence oligonucleotide 15 aaatagccgg gccgc 15 16 15 DNAArtificial Sequence oligonucleotide 16 ccagccagtc tctcc 15 17 15 DNAArtificial Sequence oligonucleotide 17 gacgacaaga ccgcg 15 18 15 DNAArtificial Sequence oligonucleotide 18 cagcctcgtc gcagc 15 19 15 DNAArtificial Sequence oligonucleotide 19 ctcgcggtcg aagcg 15 20 15 DNAArtificial Sequence oligonucleotide 20 gcgtcggtcc gggct 15 21 20 DNAArtificial Sequence oligonucleotide 21 tatgtatatt ttgtaatcag 20 22 20DNA Artificial Sequence oligonucleotide 22 ttcaagttaa acattctatc 20 2320 DNA Artificial Sequence oligonucleotide 23 tgattctacc tatgtgattt 2024 20 DNA Artificial Sequence oligonucleotide 24 gagattgttt ccctttcaaa20 25 20 DNA Artificial Sequence oligonucleotide 25 atgcaatgctacatattcgc 20 26 20 DNA Artificial Sequence oligonucleotide 26ccactatacc atctatgtac 20 27 20 DNA Artificial Sequence oligonucleotide27 ccatcattgt gtctacctca 20 28 20 DNA Artificial Sequenceoligonucleotide 28 cgggaccaac taaaggaaat 20 29 20 DNA ArtificialSequence oligonucleotide 29 tagtggcgat tagattctgc 20 30 20 DNAArtificial Sequence oligonucleotide 30 agctgcagtg gatgtgagaa 20 31 20DNA Artificial Sequence oligonucleotide 31 tacttccagt gctcagcgta 20 3220 DNA Artificial Sequence oligonucleotide 32 cagtgagaca gcaatggtcg 2033 20 DNA Artificial Sequence oligonucleotide 33 cgagcttatc cctatccctc20 34 20 DNA Artificial Sequence oligonucleotide 34 cgtactagcgttggtcatgg 20 35 20 DNA Artificial Sequence oligonucleotide 35aaggcgagtc aggctcagtg 20 36 20 DNA Artificial Sequence oligonucleotide36 accgacgacg ctgatccgat 20 37 20 DNA Artificial Sequenceoligonucleotide 37 agcagtccgc cacaccctga 20 38 20 DNA ArtificialSequence oligonucleotide 38 cagcctcgtt cgcacagccc 20 39 20 DNAArtificial Sequence oligonucleotide 39 gtggtgggcc gtgcgctctg 20 40 20DNA Artificial Sequence oligonucleotide 40 gtccacgccc ggtgcgacgg 20 4125 DNA Artificial Sequence oligonucleotide 41 gatatagcaa aattctaagttaata 25 42 25 DNA Artificial Sequence oligonucleotide 42 ataactttacgtgtgtgacc tatta 25 43 25 DNA Artificial Sequence oligonucleotide 43gttctatact cttgaagttg attac 25 44 25 DNA Artificial Sequenceoligonucleotide 44 ccctgcactt taactgaatt gttta 25 45 25 DNA ArtificialSequence oligonucleotide 45 taaccatact gaataccttt tgacg 25 46 25 DNAArtificial Sequence oligonucleotide 46 tccacacggt agtaaaatta ggctt 25 4725 DNA Artificial Sequence oligonucleotide 47 ttccaaaagg agttatgagttgcga 25 48 25 DNA Artificial Sequence oligonucleotide 48 aatatctctcatgcgccaag ctaca 25 49 25 DNA Artificial Sequence oligonucleotide 49tagtatatcg cagcatcata caggc 25 50 25 DNA Artificial Sequenceoligonucleotide 50 tggattctac tcaaccttag tctgg 25 51 25 DNA ArtificialSequence oligonucleotide 51 cggaatccat gttacttcgg ctatc 25 52 25 DNAArtificial Sequence oligonucleotide 52 ctggtctgga tctgagaact tcagg 25 5325 DNA Artificial Sequence oligonucleotide 53 acagcgaatg gacctacgtggcctt 25 54 25 DNA Artificial Sequence oligonucleotide 54 agcaagtcgagcagggccta cgttt 25 55 25 DNA Artificial Sequence oligonucleotide 55gcgagcgaca ggttacttgg ctgat 25 56 25 DNA Artificial Sequenceoligonucleotide 56 aaaggtgtcg cggagagtcg tgctg 25 57 25 DNA ArtificialSequence oligonucleotide 57 atgggtggga gcctcggtag cagcc 25 58 25 DNAArtificial Sequence oligonucleotide 58 cagtgggctc ctgggcgtgc tggtc 25 5925 DNA Artificial Sequence oligonucleotide 59 gccaactccg tcgccgttcgtgcgc 25 60 25 DNA Artificial Sequence oligonucleotide 60 acgggtccccgcaccgcacc gccag 25 61 30 DNA Artificial Sequence oligonucleotide 61ttatgtatta agttatatag tagtagtagt 30 62 30 DNA Artificial Sequenceoligonucleotide 62 attgatatcc ttttctattc atctttcatt 30 63 30 DNAArtificial Sequence oligonucleotide 63 aaagtacatc aacatagaga attgcatttc30 64 30 DNA Artificial Sequence oligonucleotide 64 cttaagatatgagaacttca actaatgtgt 30 65 30 DNA Artificial Sequence oligonucleotide65 ctcaacttgc ggtaaataaa tcgcttaatc 30 66 30 DNA Artificial Sequenceoligonucleotide 66 tattgagaac aagtgtccga ttagcagaaa 30 67 30 DNAArtificial Sequence oligonucleotide 67 gtcatacgac tgagtgcaac attgttcaaa30 68 30 DNA Artificial Sequence oligonucleotide 68 aacctgcaacatggagtttt tgtctcatgc 30 69 30 DNA Artificial Sequence oligonucleotide69 ccgtgcggtg tgtacgtttt attcatcata 30 70 30 DNA Artificial Sequenceoligonucleotide 70 gttcacgtcc gaaagctcga aaaaggatac 30 71 30 DNAArtificial Sequence oligonucleotide 71 agtctggtct ggatctgaga acttcaggct30 72 30 DNA Artificial Sequence oligonucleotide 72 tcggagaaatcactgagctg cctgagaaga 30 73 30 DNA Artificial Sequence oligonucleotide73 cttcaacgga tcaggtagga ctgtggtggg 30 74 30 DNA Artificial Sequenceoligonucleotide 74 acgcccacag gattaggctg gcccacattg 30 75 30 DNAArtificial Sequence oligonucleotide 75 gttattccgc agtccgatgg cagcaggctc30 76 30 DNA Artificial Sequence oligonucleotide 76 tcagtaggcgtgacgcagag ctggcgatgg 30 77 30 DNA Artificial Sequence oligonucleotide77 cgcgccacgt gtgatctaca gccgttcggc 30 78 30 DNA Artificial Sequenceoligonucleotide 78 gacctgacgt ggaccgctcc tgggcgtggt 30 79 30 DNAArtificial Sequence oligonucleotide 79 gcccctccac tggccgacgg cagcaggctc30 80 30 DNA Artificial Sequence oligonucleotide 80 cgccgctgccgactggagga gcgcgggacg 30 81 10 DNA Artificial Sequence oligonucleotide81 atcaatcata 10 82 10 DNA Artificial Sequence oligonucleotide 82ttgtagtcat 10 83 10 DNA Artificial Sequence oligonucleotide 83gaaatgaaag 10 84 10 DNA Artificial Sequence oligonucleotide 84ccaacttctt 10 85 10 DNA Artificial Sequence oligonucleotide 85atcgtctgga 10 86 10 DNA Artificial Sequence oligonucleotide 86agcgtaagtc 10 87 10 DNA Artificial Sequence oligonucleotide 87cgatctgcga 10 88 10 DNA Artificial Sequence oligonucleotide 88tggcgagcac 10 89 10 DNA Artificial Sequence oligonucleotide 89gatgcgctcg 10 90 10 DNA Artificial Sequence oligonucleotide 90gggaccgcct 10 91 11 DNA Artificial Sequence oligonucleotide 91cgtacacatg c 11 92 11 DNA Artificial Sequence oligonucleotide 92ccattgctac c 11

What is claimed is:
 1. A method for estimating a melting temperature(T_(m)) for a polynucleotide at a desired ion concentration [X⁺], saidpolynucleotide having a known G-C content value, ƒ(G-C), comprising: (a)obtaining a reference melting temperature (T_(m) ⁰) for thepolynucleotide, said reference melting temperature being a meltingtemperature obtained or provided for the polynucleotide at a referenceion concentration [X⁺]₀; and (b) modifying the reference meltingtemperature by a logarithm of the ratio of said desired ionconcentration to said reference ion concentration, said logarithm beingmultiplied by a coefficient which is a function of the G-C contentvalue, wherein the estimated melting temperature is calculated using thereference melting temperature.
 2. A method for estimating a meltingtemperature (T_(m)) for a polynucleotide at a desired ion concentration[X⁺], said polynucleotide having a known G-C content value, ƒ(G-C),comprising: (a) obtaining a reference melting temperature (T_(m) ⁰) forthe polynucleotide, said reference melting temperature being a meltingtemperature obtained or provided for the polynucleotide at a referenceion concentration [X⁺]₀; and (b) modifying the reference meltingtemperature by an amount,${k( {f( {G - C} )} )} \times \ln \frac{\lbrack X^{+} \rbrack}{\lbrack X^{+} \rbrack_{0}}$

in which the coefficient k(ƒ(G-C) ) is a function of the G-C contentvalue ƒ(G-C), wherein the estimated melting temperature is obtained byusing the reference melting temperature.
 3. The method of claim 2,wherein the coefficient k has a value determined by the relationk(ƒ(G-C))=m·ƒ(G-C)+k ₀; and wherein a first coefficient, m and a secondcoefficient, k₀, are optimized for predicting polynucleotide meltingtemperatures T_(m) ⁰.
 4. The method of claim 2, wherein the referencemelting temperature T_(m) ⁰ is used to calculate T_(m) according to theformula:$T_{m} = {T_{m}^{0} + {k \times \ln {\frac{\lbrack X^{+} \rbrack}{\lbrack X^{+} \rbrack_{0}}.}}}$


5. The method of claim 4, wherein the coefficient kk(ƒ(G-C))=m·ƒ(G-C)+k₀; and wherein a first coefficient, m and a secondcoefficient, k₀ are optimized for predicting polynucleotide meltingtemperatures T_(m) ⁰.
 6. The method of claim 2, wherein the referencemelting temperature T_(m) ⁰ is used to calculate T_(m) according to theformula:$T_{m} = {T_{m}^{0} + {{k( {f( {G - C} )} )} \times \ln \frac{\lbrack X^{+} \rbrack}{\lbrack X^{+} \rbrack_{0}}} + {b \times {( {{\ln^{2}\lbrack X^{+} \rbrack} - {\ln^{2}\lbrack X^{+} \rbrack}_{0}} ).}}}$


7. The method of claim 6, wherein k is m·ƒ(G-C)+k₀; and wherein a firstcoefficient, m, a second coefficient, k₀ and a third coefficient b areoptimized for predicting polynucleotide melting temperatures T_(m) ⁰. 8.The method according to claim 5, wherein m is −3.22, k₀ is 6.39.
 9. Themethod according to claim 7, wherein m is −4.62, k₀ is 4.52 andb=−0.985.
 10. The method of claim 2, wherein the reference meltingtemperature T_(m) ⁰ is used to calculate T_(m) according to the formula:$\frac{1}{T_{m}} = {\frac{1}{T_{m}^{0}} + {{k( {f( {G - C} )} )} \times \ln {\frac{\lbrack X^{+} \rbrack}{\lbrack X^{+} \rbrack_{0}}.}}}$


11. The method of claim 10, wherein the coefficient k has a determinedvalue by the relation kƒ(G-C))=m·ƒ(G-C)+k₀; and wherein a firstcoefficient, m and a second coefficient, k₀ are optimized for predictingpolynucleotide melting temperatures.
 12. The method of claim 2, whereinthe melting temperature is obtained from the reference T_(m) ⁰ byutilizing the formula:$\frac{1}{T_{m}} = {\frac{1}{T_{m}^{0}} + {{k( {f( {G - C} )} )} \times \ln \frac{\lbrack X^{+} \rbrack}{\lbrack X^{+} \rbrack_{0}}} + {b \times {( {{\ln^{2}\lbrack X^{+} \rbrack} - {\ln^{2}\lbrack X^{+} \rbrack}_{0}} ).}}}$


13. The method of claim 10, wherein k is m·ƒ(G-C)+k₀; and wherein afirst coefficient, m and a second coefficient, k₀ and a thirdcoefficient b are optimized for predicting polynucleotide meltingtemperature.
 14. The method of claim 11, wherein k₀ is −6.18×10⁻⁵; m is3.85×10⁻⁵.
 15. The method of claim 13, wherein k₀ is −3.95×10⁻⁵; m is4.29×10⁻¹; and b is 9.40×10⁻⁶.
 16. The method of claim 2, wherein theG-C content value is the fraction of the polynucleotide's nucleotidebases that are either guanine or cytosine.
 17. The method of claim 1,wherein the polynucleotide is DNA.
 18. The method of claim 1, whereinthe polynucleotide ranges in length from about 2 to about 500 basepairs.19. The method of claim 1, wherein the polynucleotide ranges in lengthfrom about 5 to about 200 base pairs.
 20. The method of claim 1, whereinthe polynucleotide ranges from about 10 to about 30 basepairs in length.21. The method of claim 1, wherein the reference melting temperature isexperimentally determined.
 22. The method of claim 1, wherein thereference melting temperature is calculated from a theoretical model.23. The method of claim 1, wherein the reference melting temperature isobtained by utilizing a nearest neighbor model.
 24. The method of claim1, wherein the reference ion concentration is 1 M.
 25. The method ofclaim 1, wherein the ion is a monovalent ion.
 26. The method of claim 1,wherein the ion is selected from the group consisting of the cations ofsodium, lithium, potassium, rubidium, cesium and francium.
 27. Themethod of claim 1, wherein the desired ion concentration ranges betweenabout 1 mM and about 5M.
 28. The method of claim 1, wherein the desiredion concentration ranges between about 10 mM and about 2M.
 29. Themethod of claim 1, wherein the desired ion concentration ranges betweenabout 70 mM and about 1021 mM.
 30. A computer system for predicting amelting temperature, which computer system comprises: (a) a memory; and(b) a processor interconnected with the memory and having one or moresoftware components loaded therein, wherein the one or more softwarecomponents cause the processor to execute steps of a method according toclaim
 1. 31. A computer program product comprising a computer readablemedium having one or more software components encoded thereon incomputer readable form, wherein the one or more software components maybe loaded into a memory of a computer system and cause a processorinterconnected with said memory to execute steps of a method accordingto claim 1.